ÉCOLE DE TECHNOLOGIE SUPÉRIEURE UNIVERSITÉ DU QUÉBEC ...³bal.pdf · Mr. Wael Suleiman,...
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ÉCOLE DE TECHNOLOGIE SUPÉRIEURE UNIVERSITÉ DU QUÉBEC MANUSCRIPT-BASED THESIS PRESENTED TO ÉCOLE DE TECHNOLOGIE SUPÉRIEURE IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Ph.D. BY Cristóbal OCHOA LUNA NONLINEAR CONTROL OF A SEVEN DEGREES-OF-FREEDOM EXOSKELETON ROBOT ARM MONTREAL, MARCH 21, 2016 © Copyright Cristóbal Ochoa Luna, 2016 All rights reserved
Transcript of ÉCOLE DE TECHNOLOGIE SUPÉRIEURE UNIVERSITÉ DU QUÉBEC ...³bal.pdf · Mr. Wael Suleiman,...
ÉCOLE DE TECHNOLOGIE SUPÉRIEURE UNIVERSITÉ DU QUÉBEC
MANUSCRIPT-BASED THESIS PRESENTED TO ÉCOLE DE TECHNOLOGIE SUPÉRIEURE
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
Ph.D.
BY Cristóbal OCHOA LUNA
NONLINEAR CONTROL OF A SEVEN DEGREES-OF-FREEDOM EXOSKELETON ROBOT ARM
MONTREAL, MARCH 21, 2016
© Copyright Cristóbal Ochoa Luna, 2016 All rights reserved
© Copyright
Reproduction, saving or sharing of the content of this document, in whole or in part, is prohibited. A reader
who wishes to print this document or save it on any medium must first obtain the author’s permission.
BOARD OF EXAMINERS
THIS THESIS HAS BEEN EVALUATED
BY THE FOLLOWING BOARD OF EXAMINERS Mr. Maarouf Saad, Thesis Supervisor Department de genie électrique, École de technologie supérieure Mr. Guy Gauthier, Chair, Board of Examiners Département de génie de la production automatisée, École de technologie supérieure Mr. Vahé Nerguizian, Member of the jury Département de génie électrique, École de technologie supérieure Mr. Philippe S. Archambault, Member of the jury School of Physical & Occupational Therapy, McGill University and Centre of Interdisciplinary Research in Rehabilitation (CRIR) Mr. Wael Suleiman, Independent External Evaluator Electrical and Computer Engineering Department, Engineering Faculty, Université de Sherbrooke
THIS THESIS WAS PRESENTED AND DEFENDED
IN THE PRESENCE OF A BOARD OF EXAMINERS AND THE PUBLIC
ON JANUARY 21, 2016
AT ÉCOLE DE TECHNOLOGIE SUPÉRIEURE
FOREWORD
The present work is part of the project that has as final objective to develop an upper arm
robotic exoskeleton to perform a variety of rehabilitation tasks as well as help in daily life
activities. Design and construction of the robot as well as the first control approaches and
passive rehabilitation schemes were developed in the work of Mohammad H. Rahman in his
Ph.D. studies at École de technologie supérieure (ETS), research summarized in the thesis
cited below. Also the work of Thierry Kittel-Ouimet in his M.Sc. studies at ETS yielding to
the thesis also cited below.
1. Kittel-Ouimet, Thierry. 2012. « Commande d'un bras exosquelette robotique à sept
degrés de liberté ». Master in electric engineering thesis. Montréal, École de technologie
supérieure, 154 p.
2. Rahman, Mohammad Habibur. 2012. « Development of an exoskeleton robot for
UPPER-LIMB rehabilitation ». Doctor of Philosophy thesis. Montréal, École de
technologie supérieure, 206 p.
ACKNOWLEDGMENTS
I wish to express my deepest gratitude to my advisor, Dr. Maarouf Saad for all his teachings
and the shared knowledge; but especially his invaluable guidance, patience and his enormous
qualities as a mentor and as a person. Without them, the achievement of the present work
would have not been possible.
I want to thank as well all my research team: Dr. Philippe S. Archambault, Dr. Jawhar
Ghommam, Dr. Wen-Hong Zhu, Dr. Mohammad H. Rahman, Abdelkrim Brahmi, Thierry
Kittel-Ouimet and Bruce S. Ferrer for their important contributions to this research. Also I
want to thank Dr. Guy Gauthier, Dr. Aimé Francis Okou and Dr. Ilian Bonev for their
teaching during the initial part of my studies. I wish to express my gratitude to Dr. Maarouf
Saad, Dr. Guy Guthier, Dr. Philippe S. Archambault, Dr. Vahé Nerguizian and Dr. Wael
Suleiman for being part of the committee who agreed to review and evaluate this research
work. Thanks to Dr. Kash Khorasani for his contribution in my education.
I would like to thank the National Council on Science and Technology of Mexico
(CONACYT) for the support under grant No. 211951 jointly with Professor Maarouf Saad
and École de technologie supérieure, for the most part of my studies. As well as for the
important financial support that Dr. Saad provided in the final part of my studies.
Overall, I want to express my warmest thanks to my parents and sister for their unconditional
love and support in all possible ways. To the rest of my family that always supported me in
many different means, welcomed me on vacations with all the affection and warmness and
forgave the extremely short time that I could spent with them during the last six years.
My most sincere thanks to my friends, back in Mexico and the ones that I made here in
Canada; for sharing so many fun and stress-relieving moments, as well as the support and
encouragement.
COMMANDE NON LINÉAIRE D'UN BRAS EXOSQUELETTE ROBOTIQUE À SEPT DEGRÉS DE LIBERTÉ
Cristóbal OCHOA LUNA
RÉSUMÉ
Les progrès dans le domaine de la robotique ont permis l’intégration de plus en plus de dispositifs robotisés pour la réadaptation des personnes avec un handicap physique. Ce travail de recherche englobe tout le domaine de la robotique de réadaptation; il présente l’évolution du robot ETS-MARSE, un exosquelette à sept degrés de liberté destiné à être porté par le bras humain. Les développements incluent l’étude et l’implémentation d’une approche de contrôle non linéaire relativement nouvelle, ainsi que différents programmes de réadaptation. Une des caractéristiques d’un robot de réadaptation est qu’il est utilisé par un grand nombre de patients qui ont des conditions physiologiques et biomécaniques diverses. L’implémentation de la technique de contrôle non linéaire, connue sous le nom de Virtual Decomposition Control, atteint cette exigence grâce à son adaptation de paramètres internes qui présente un comportement robuste pour les différentes caractéristiques des utilisateurs de robot. En outre, cette technique simplifie la complexité des robots possédant de hauts degrés de liberté par son innovante décomposition du système. De plus, elle lui assure une stabilité asymptotique et un excellent suivi de trajectoires. Parmi les différents programmes de réadaptation, nous pouvons nommer : la réadaptation passive, la réadaptation active-assistée et la réadaptation active. La première suit des trajectoires prédéfinies et s’appuie sur l’efficacité du dispositif de commande. Les deux autres programmes ont besoin d’une méthode de compréhension de l’intention du mouvement de l’utilisateur; ils peuvent donc prendre une action de suivre, guider, retenir ou corriger le mouvement. À cet effet, notre première approche utilise un capteur de force comme l’interface humain-robot afin de transformer, par l’intermédiaire d’une fonction d’admittance, les forces que l’utilisateur exerce sur l’effecteur du robot et exécuter la réadaptation active-assistée ou la réadaptation active. Enfin, entre les principaux développements de ce travail, une approche est présentée, dans laquelle la nécessité d’un capteur de force pour effectuer certaines tâches de réadaptation active est supprimée. Au moyen d’un observateur non linéaire, les forces d’interaction sont estimées et l’intention de mouvement de l’utilisateur s’ensuit. Les résultats expérimentaux montrent l’efficacité de toutes les approches proposées. Tous les essais qui ont été faits sur des humains ont été testés avec des sujets qui ne présentent aucun handicap. Le suivi de trajectoires du robot est exécuté dans l’espace articulaire; certaines trajectoires sont données dans l’espace cartésien et transformées à l’espace articulaire en utilisant la technique du pseudo-inverse de la matrice jacobienne. Cependant, cette option est limitée; la prochaine étape obligatoire pour améliorer les nombreuses fonctions du robot est de résoudre sa cinématique inverse. Parmi les autres progrès qui sont en développement, l’une d’entre
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elle est une approche pour la classification et la modélisation des signaux électromyographiques afin d’obtenir des informations auprès des utilisateurs du robot. Les premiers résultats utilisant cette méthodologie sont présentés. La téléopération et les capacités haptiques sont également dans la phase initiale de développement. Mots-clés: 7DDL réadaptation exosquelette, Virtual Decomposition Control, réadaptation active, réadaptation active-assistée, admittance, observateur non linéaire
NONLINEAR CONTROL OF A SEVEN DEGREES-OF-FREEDOM EXOSKELETON ROBOT ARM
Cristóbal OCHOA LUNA
ABSTRACT
Advances in the field of robotics have allowed increasingly integrating robotic devices for rehabilitation of physical disabilities. This research work is encompassed into the field of rehabilitation robotics; it presents the development of the robot ETS-MARSE, a seven degrees-of-freedom exoskeleton designed to be worn in the human arm. The developments include the study and implementation of a relatively novel nonlinear control approach, as well as different rehabilitation schemes. One of the characteristics of a rehabilitation robot is that it deals with a wide number of patients that have different biomechanical and physiological conditions. The implementation of the nonlinear control technique known as Virtual Decomposition Control addresses this issue with its internal parameters’ adaptation that presents a robust behavior to different characteristics of the robot users. Besides, this technique simplifies the complexity of high degree-of-freedom robots by its innovative sub-systems decomposition. All of above, while ensuring the system asymptotic stability and excellent trajectory tracking. Between the different rehabilitation schemes, we can mention: passive, active-assistive and active rehabilitation. The first one follows predefined trajectories and relies on the efficiency of the controller. The two other schemes require understanding the user’s intention of movement and take an action in order to guide, restrain, correct or follow it. For this purpose, we present an approach that utilizes a force sensor as the human-robot interface in order to transform, via an admittance function, the forces that the user exert to the robot end-effector (handle), and execute active-assisted or active rehabilitation. Finally among the main developments of this work, an approach is presented in which the need of a force sensor to perform some active rehabilitation tasks is removed. By means of a nonlinear observer, the interaction forces are estimated and the user’s intention of movement followed. Experimental results show the effectiveness of all the proposed approaches. All the tests involving humans were tested with healthy subjects. Trajectory tracking of the robot is executed in joint space; some trajectories are given in Cartesian space and transformed to joint space by means of the pseudoinverse of the Jacobian technique. However this option is limited; a mandatory next step to improve many functionalities of the robot is to solve its inverse kinematics. Between other progresses that are in development, is an approach to process electromyographic signals in order to obtain information from the robot’s users. First results on this methodology are presented. Teleoperation and haptic capabilities are also in the initial stage of development.
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Keywords: 7DOF rehabilitation exoskeleton, Virtual Decomposition Control, active rehabilitation, active-assistive rehabilitation, admittance, nonlinear observer
TABLE OF CONTENTS
Page
INTRODUCTION .....................................................................................................................1
CHAPTER 1 RESEARCH PROBLEM .............................................................................5 1.1 Literature review ............................................................................................................6
1.1.1 Overview of control inputs and control strategies ...................................... 7 1.1.2 End-effector type upper-limb rehabilitation robots state of the art ............. 8 1.1.3 Exoskeleton type upper-limb rehabilitation state of the art robots ............. 9 1.1.4 Limitations of current approaches ............................................................ 10
1.2 Research objectives and methodology .........................................................................10 1.2.1 Development of the nonlinear control law ................................................ 11 1.2.2 The sensing interface ................................................................................ 11 1.2.3 Inverse Kinematics.................................................................................... 11 1.2.4 Implementation and experimentation ....................................................... 12
1.3 Originality of the research and contribution ................................................................12
CHAPTER 2 VIRTUAL DECOMPOSITION CONTROL OF AN EXOSKELETON ROBOT ARM ..............................................................15
2.1 Introduction ..................................................................................................................16 2.2 Characteristics of the Motion Assistive Robotic Exoskeleton for
Superior Extremity .......................................................................................................20 2.3 Analysis of the ETS-MARSE robot with Virtual Decomposition Control
(Zhu et al., 1997) ..........................................................................................................22 2.3.1 Kinematics ................................................................................................ 23 2.3.2 Dynamics .................................................................................................. 25 2.3.3 Control ...................................................................................................... 29 2.3.4 Stability Analysis ...................................................................................... 31
2.4 Experimental Results ...................................................................................................34 2.4.1 Varying subjects experiment ..................................................................... 35 2.4.2 Varying velocity experiment..................................................................... 40 2.4.3 Active rehabilitation experiment ............................................................... 42 2.4.4 Parameter adaptation ................................................................................. 43 2.4.5 Discussion of experimental results ........................................................... 45 2.4.6 Safety ........................................................................................................ 45
2.5 Conclusions and Future Work .....................................................................................46
CHAPTER 3 ADMITTANCE-BASED UPPER LIMB ROBOTIC ACTIVE AND ACTIVE-ASSISTIVE MOVEMENTS .....................................................49
3.1 Introduction ..................................................................................................................50 3.2 System Overview .........................................................................................................53 3.3 Virtual Decomposition Control of the ETS-MARSE ..................................................55
3.3.1 Robot subsystem decomposition .............................................................. 57
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3.3.2 Kinematics ................................................................................................ 57 3.3.3 Dynamics .................................................................................................. 59
3.4 Active-assistive and active rehabilitation ....................................................................63 3.4.1 Trajectory planner ..................................................................................... 63 3.4.2 Active-assistive rehabilitation based on an admittance-modified
trajectory planner ...................................................................................... 65 3.4.3 Active rehabilitation based on an admittance-modified
trajectory planner ...................................................................................... 66 3.5 Experimental results.....................................................................................................70
3.5.1 Active-assistive rehabilitation ................................................................... 70 3.5.2 Active rehabilitation, constrained free movement .................................... 73
3.6 Conclusions ..................................................................................................................76
CHAPTER 4 COMPLIANT CONTROL OF A REHABILITATION EXOSKELETON ROBOT ARM WITH FORCE OBSERVER ...............77
4.1 Introduction ..................................................................................................................78 4.2 Nonlinear control: Virtual Decomposition Control and Force Observer .....................81
4.2.1 Nonlinear force observer ........................................................................... 81 4.2.2 Stability Analysis ...................................................................................... 85 4.2.3 Admittance control .................................................................................... 87
4.3 Experimental results.....................................................................................................88 4.3.1 System architecture ................................................................................... 88 4.3.2 Joint space task ......................................................................................... 90 4.3.3 Cartesian space task .................................................................................. 93
4.4 Conclusions ..................................................................................................................95
DISCUSSION OF THE RESULTS .........................................................................................97
CONCLUSION ....................................................................................................................99
RECOMMENDATIONS .......................................................................................................101
ANNEX I ADITIONAL AND FUTURE WORK: ELECTROMYOGRAPHY, TELEOPERATION AND HAPTIC CAPABILITIES ............................109
ANNEX II VIRTUAL DECOMPOSITION CONTROL ..........................................115
BIBLIOGRAPHY ..................................................................................................................121
LIST OF TABLES
Page Table 1.1 End-effector type upper-limb rehabilitation state-of-the-art robots .............8
Table 1.2 Exoskeleton type upper-limb rehabilitation state-of-the-art robots .............9
Table 2.1 ETS-MARSE Modified Denavit-HartenbergParameters ...........................22
Table 2.2 Varying subjects experiment range of motion ...........................................37
Table 2.3 Statistical analysis of performance variation .............................................39
Table 2.4 RMS error of varying velocity experiments ..............................................40
Table 3.1 ETS-MARSE Denavit-Hartenberg modified parameters ..........................56
Table 3.2 Robot active-assistive rehabilitation reference trajectory ..........................71
Table 4.1 ETS-MARSE Denavit-Hartenberg modified parameters ..........................82
LIST OF FIGURES
Page
Figure 1.1 Methodology ..............................................................................................12
Figure 2.1 Joint range of motion of ETS-MARSE ......................................................20
Figure 2.2 7DOF Exoskeleton robot arm ....................................................................21
Figure 2.3 Virtual decomposition into 14 subsystems ................................................23
Figure 2.4 Block diagram of the system (with the equations used in each step in the parentheses)......................................................................................30
Figure 2.5 ETS-MARSE with human subject .............................................................34
Figure 2.6 Experimental setup with control architecture ............................................35
Figure 2.7 Schematic diagram, reaching movement exercise .....................................36
Figure 2.8 RMS joint tracking error along the 28 tests for each controller ................38
Figure 2.9 Average (joint 1 to joint 5) RMS error of each test ...................................39
Figure 2.10 VDC results for different speeds test .........................................................41
Figure 2.11 PID results for different speeds test ...........................................................41
Figure 2.12 Experimental setup for active rehabilitation ..............................................42
Figure 2.13 Cartesian trajectory, forces and torques for active rehabilitation ..............43
Figure 2.14 Left: Robot initial position. Right: Joint 4 trajectory .................................44
Figure 2.15 Parameter adaptation of joint 4 ..................................................................44
Figure 3.1 Subject wearing ETS-MARSE robot arm ..................................................54
Figure 3.2 ETS-MARSE system hardware overview .................................................55
Figure 3.3 7DOF exoskeleton robot arm .....................................................................56
Figure 3.4 Virtual decomposition in 14 subsystems ...................................................57
Figure 3.5 Block diagram of the VDC ........................................................................62
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Figure 3.6 Block diagram of the system......................................................................67
Figure 3.7 Active rehabilitation with walls .................................................................68
Figure 3.8 Virtual wall collision and reset path ..........................................................69
Figure 3.9 Active-assisted rehabilitation with walls ...................................................69
Figure 3.10 Reference trajectory tracking .....................................................................70
Figure 3.11 Trajectory modified with high degree of help ...........................................72
Figure 3.12 Trajectory modified with low degree of help ............................................72
Figure 3.13 Comparison of forces-torques between high and low degree of assistance from the robot ...........................................................73
Figure 3.14 Virtual walls as obstacle for active rehabilitation ......................................74
Figure 3.15 Virtual walls as obstacle and starting point for robotic assistance in active rehabilitation ................................................................................75
Figure 4.1 7DOF exoskeleton robot arm .....................................................................82
Figure 4.2 Subject wearing ETS-MARSE robot arm and virtual interface .................90
Figure 4.3 Joint space exercises ..................................................................................91
Figure 4.4 Joint space exercise estimated torques and joint positions ........................91
Figure 4.5 Joint 3 position and estimated and measured force for joint space test .....92
Figure 4.6 Cartesian space trajectory test results ........................................................93
Figure 4.7 Measured and estimated position and position error .................................94
LIST OF ABBREVIATIONS AND ACRONYMS DOF Degrees-of-freedom CRIR Interdisciplinary Research Center in Rehabilitation CTC Computed Torque Control DC Direct Current EBC Electromyographic Based Control EMG Electromyographic ETS École de technologie supérieure FBC Force Based Control FPGA Field Programmable Gate Array HMI Human Machine Interface MARSE Motion Assistive Robotic-exoskeleton for Superior Extremity mDH Modified Denavit-Hartenberg parameters PD Proportional-Derivative PI Proportional-Integral PID Proportional-Integral-Derivative RMS Root-Mean-Square SMC Sliding Mode Control SCARA Selective Compliant Assembly (or Articulated) Robot Arm UE Upper Extremity US United States VDC Virtual Decomposition Control
LIST OF SYMBOLS AND UNITS OF MEASUREMENTS UNITS OF MEASUREMENT ° or deg degree µs microsecond σ standard deviation A ampere cm centimeter g gram Kg kilogram m meter mNm millinewton meter ms millisecond N newton Nm newton meter rpm revolutions per minute s or sec second V volt W watt SYMBOLS αi-1 angle from to , measured about
ai-1 length from to , measured about
di distance from to measured about
θi joint angle from to measured positive about
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, , Unitary vectors of the Cartesian coordinate system main axes. force/moment transformation matrices from frame to frame linear/angular velocity vector of frame { }
augmented velocity vector
VDC Jacobian matrix
augmented required velocity vector
link parameters vector
estimated parameters vector ∗ required net force/moment vector required force/moment vector ∗ net torque for the joint
link force/moment vector
control torque in Nm
INTRODUCTION
Since the beginnings of robotics, robots have been associated with human beings. In fact,
their first activity was their use in the industrial environment to replace or help people in
repetitive, dangerous or tedious tasks, and those that require high precision. Subsequently the
relation was enriched with a greater exchange of information, for example in areas as robot
teleoperation and service robots; nowadays, the relation has arrived at the level of cognitive
and physical interaction in the called wearable robots. These robots can be defined as: “those
worn by human operators, whether to supplement the function of a limb or to replace it
completely” (Pons, 2008).
We can classify wearable robots into two general types, prosthetic and orthotic robots. The
first ones have the purpose of replacing a member lost by amputation; the second ones, also
called exoskeletons, map the structure of the limb and adapt to it to re-establish or to
complete some functional lost. Among the purposes for the wearable robots we can mention:
the increase of power, e.g. military applications; teleoperation, e.g. aerospace industry; and
rehabilitation, in which our research work is focused. Additionally we can classify them, in a
general way, as upper-limb and lower-limb exoskeletons, depending if they are worn in the
arms or in the legs respectively.
This thesis presents the development of a robotic orthosis for the upper-limb to be used in
rehabilitation, the robot ETS-MARSE (Motion Assistive Robotic-exoskeleton for Superior
Extremity). The ETS-MARSE has seven degrees of freedom (DOF) designed to correspond
with the main DOF of the human arm at shoulder (3DOF), elbow (1DOF) and wrist (3DOF)
levels. The developments included in this work are the study and implementation of a novel
control approach and some passive, active-assisted and active rehabilitation schemes. In
rehabilitation when assistance is mandatory or might be needed, a therapist, apparatus or
robot could participate; in our case, the proposed robot will be in charge of the assistance
according to the necessary rehabilitation scheme. Passive rehabilitation is the kind of
rehabilitation in which the subject should not provide effort and the rehabilitation task is
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carried out by the robot. Active-assisted rehabilitation is the kind of rehabilitation where the
subject receives partial assistance from the robot. In active rehabilitation, the subject
performs the exercise by itself and the robot became the object of the exercise and an
excellent way to measure the subject’s performance.
The ETS-MARSE is commanded in passive mode by pre-generated trajectories, either in
joint space or Cartesian space, which correspond to different rehabilitation exercises. In
active-assisted mode the predefined trajectory is followed by the robot, but it is allowed to be
modified by the user in variable degrees. In active mode, the robot responds to the user
intention of movement by following it and only assists according with time and spatial
constrains.
The first chapter of this document describes the research problem. First, the chapter presents
the identification and justification of the research problem, where the problematic that
validates the present project is presented. A review of the existing literature is given and the
outline of the state of the art of this area of research. Immediately, the objectives of the
project, so much general as specific, are declared. Finally, it is presented an overview of the
methodology used.
The second chapter presents the first paper of this research work. It is called “Virtual
Decomposition Control of an Exoskeleton Robot Arm” and was published in Robotica in
October, 2014 (Ochoa Luna et al., 2014b) (on-line version). This paper deals with two
important issues in rehabilitation robotics: The first one is the capacity to adapt to different
patients without significantly varying its performance. It is demonstrated that VDC through
its internal parameter adaptation is capable to adapt to the whole robot-human system and
have a robust behavior in comparison with Computed Torque control and PID control. The
second is that with the novel subsystem decomposition of the VDC, the dynamics of the
ETS-MARSE (a 7DOF robot) results in simpler dynamics to be handled by the control
computation.
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The third chapter is the second journal paper titled “Admittance-Based Upper Limb Robotic
Active and Active-Assistive Movements” and was published online in the International
Journal of Advanced Robotic Systems in September, 2015 (Ochoa Luna et al., 2015). It deals
with the first approach to active-assisted and active rehabilitation modes. Both approaches
uses the VDC control encompassed in a compliant control. The active-assistive approach
uses the virtual work principle and an admittance function to transform the measurements
from a force sensor (in the handle of the robot) into trajectory variations that allows the
system to understand the user’s intention of movement. The admittance is anchored to a
predefined trajectory; this allows, by changing its coefficients (spring and damping) to
provide more or less degree of help to the user. In the active approach, this anchor is
detached and the force transformation results on real-position differentials instead of
trajectory ones; allowing the subject to move freely in space. A virtual environment is
presented to guide the movement in the first case and in the second to restrain the free
environment by virtual walls.
The fourth chapter contains the third research paper titled “Compliant Control of a
Rehabilitation Exoskeleton Robot Arm with Force Observer” that was send to the
IEEE/ASME Transactions on Mechatronics in March 2016. In our research we realised that
the use of a force sensor to guide the movements of the robot, especially at the handle level,
could easily result in the damage of such sensor. Also the high cost of elaborated sensors
presents a problem for this kind of robots, among other complications. This third paper
shows how a nonlinear observer could be used to estimate the user intention of movement
instead of a force sensor. The observer successfully estimates the interaction forces between
the subject and the robot, and uses this information through a compliant control, as in the
second paper, to follow the user’s intention of movement.
After, the discussion of the results and the conclusion of the thesis based in the manuscripts
described above are given. Finally, to present the additional content, Annex I presents results
of this research that were not encompassed in the three main papers product of this thesis; as
well as the present and future work for the ETS-MARSE. Between the results shown is an
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approach to process and read information from electromyographic (EMG) signals. This
method was used in another journal paper: “EMG Based Control of a Robotic Exoskeleton
for Shoulder and Elbow Motion Assist”, published in the Journal of Automation and Control
Engineering in 2015 (Rahman et al., 2015a); as well as in combination with the force sensor
control described in Chapter 3, in the paper: “Force-Position Control of a Robotic
Exoskeleton to Provide Upper Extremity Movement Assistance” published in the
International Journal of Modelling Identification and Control in 2014 (Rahman et al., 2014).
The EMG approach is also used in the development of a Neuro-Fuzzy controller to command
the ETS-MARSE with the EMG signals from the user’s arm. An approach using a haptic
device for teleoperation and eventually haptic capabilities for the ETS-MARSE is also
described. Annex II presents an overview (not centered in the ETS-MARSE) of the
implementation of VDC for manipulator-like robots.
CHAPTER 1
RESEARCH PROBLEM
In everyday life as consequence of traumas, accidents, work-related injuries, geriatric
disorders, sport injuries, among others, diverse types of physiological consequences exist that
bring limitations of diverse kind. Between them we can mention: social, occupational, and
personal, that result into a decrease in the quality of life of large number of people. Among
the main causes, one of the more important nowadays is stroke; it is considered by the World
Health Organization (WHO) as a global epidemic. According with the WHO each year 15
million people suffer a stroke worldwide; of them 5 million die and another 5 million are left
permanently disabled (Mackay and Mensah, 2004). In Canada, the amount of people
suffering consequences of stroke is very large. In 2003, the number of people from 12 years
of age and older that were living with the effects of a stroke was 272 000; and yearly,
between 40 000 and 50 000 are hospitalized by this condition (Health Canada, 2006).
Among the survivors of a stroke often a burden is placed on their life (physical, emotional
and cognitive effects). One of the most common effects after a stroke is weakness or inability
to move one side of the body (hemiparesis), which affects up to 90 percent of stroke
survivors (Van der Loos and Reinkensmeyer, 2008). Spasticity affects roughly 40 percent of
stroke survivors, and is characterized by stiff or tight muscles that constraint movement
(National Stroke Association®, 2012). The main treatment for these cases is rehabilitation:
the process of helping a patient to achieve the highest level of independence and quality of
life possible. When rehabilitation is possible, implies many hours of highly skilled and
extensive physiotherapy procedures; the amount of people that can bring this support are not
sufficient to carry out with all the patients (Bureau of Labor Statistics, 2015; Gupta, Castillo-
Laborde and Landry, 2011; Landry, Ricketts and Verrier, 2007). Hence, the use of robots in
rehabilitation is a very important point of interest; in fact, in rehabilitation for the arm for
example, it has shown promising results (Klamroth-Marganska et al., 2014; Norouzi-
Gheidari, Archambault and Fung, 2012; Patton et al., 2006). The aim of the proposed
exoskeleton is to be able to supply robotic rehabilitation and contribute to help people to
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reduce the disability consequences or the disability period and make a significant
improvement on their quality of life.
1.1 Literature review
The idea to utilize orthoses is not a recent idea. In 1883 professor H. Wangenstein stated the
concept of a light-weight exoskeleton that would allow to walk about normality, designed
with the purpose that the scientists with some injuries that cannot be healed could continue
their noble work, controlled by the power of the user’s mind (Pons, 2008). This description,
referred to a pneumatic orthosis for the legs, can be considered as the first one where the
characteristics existing in the current exoskeletons developments were mentioned.
The studies in the field of upper-limb robotic rehabilitation, the subject of this research work,
have been conducted since the middle of the 20th century. The first rehabilitation robots
came in the 60’s and early 70’s with the Case Western University Arm and the Rancho Los
Amigos Golden Arm (drove joint by joint by a series of tongue-operated switches)
respectively (Siciliano and Khatib, 2008). In the mid 70’s in the Department of Veterans
Affairs the first command type interface appeared (Seamone and Schmeisser, 1985). In
relatively recent dates, an increase number of efficient experimental implementations of
rehabilitation robots for the upper-limb have been obtained; among them, there are still
different purposes and diverse number of human joints actuated. We find some examples that
are focused only on the hand (Chiri et al., 2012; Hu et al., 2013; Jiang et al., 2005; Wege,
Kondak and Hommel, 2006), that is by itself a very complex area. Some others are focused
in just some of the degrees of freedom of the arm, like elbow (Hu et al., 2007; Vitiello et al.,
2013) or wrist training (Hu et al., 2009; Krebs et al., 2007). Some are combined, as shoulder
and elbow (Masiero et al., 2007) or forearm and wrist (Gopura and Kiguchi, 2007) or elbow,
forearm and wrist (Rocon et al., 2007). Finally there are some robots, as the ETS-MARSE,
that deal with the entire arm (shoulder, elbow, forearm and wrist), which will be described in
the next subsections of this chapter. Besides rehabilitation, we have upper-limb orthoses for
purposes like power augmentation (Kazerooni and Guo, 1993; Sankai, 2006) or as haptic
7
devices for virtual reality and teleoperation (Tsagarakis, Caldwell and Medrano-Cerda,
1999).
In the study of the state of the art that follows, only robots that are aimed to provide
rehabilitation to the whole arm (shoulder, elbow, forearm and wrist) are mentioned. We
classify them into two main types: end-effector type and exoskeleton type. The first ones
attach to the human arm at specific contact points and manipulate it by applying forces to the
distal segments of the arm; the second ones, are designed to be worn by the users and model
the human arm mechanics and axis of movement. This analysis starts with a brief description
of the main approaches in control inputs and control strategies.
1.1.1 Overview of control inputs and control strategies
The source that commands the robot behavior has evolved greatly since the first
developments in the area. It has advanced through joysticks, sensors operated by another part
of the body, preprogrammed routines and others, to reach nowadays high-order schemes that
mimic with human physiological actions and responses. Two of the techniques most used in
our days are force control (Perry and Rosen, 2006) and EMG-based control. Work in the
subject of EMG signals has shown that an active EMG-driven robotic rehabilitation has some
advantages over the passive robotic rehabilitation; e.g. reducing the spasticity on the elbow
joint compared against passive rehabilitation (Hu et al., 2008). Also, the use of EMG signals
to study the arm motion provided an improve continuous-profile of force and motion
(Artemiadis and Kyriakopoulos, 2008), over previous work that deals only with the initiation
and ending of the motion.
With respect to the control strategies, we can find PD controllers used in combination with
nonlinear techniques as Computed Torque Control (CTC) (Brackbill et al., 2009), Neuro-
Fuzzy controllers (Rahman et al., 2006), Fuzzy Controllers based on Sliding Mode (Sun, Sun
and Feng, 1999), CTC combined with Fuzzy Control (Song et al., 2005) to overcome the
CTC disadvantage of requiring precise knowledge of the dynamical model of the robot.
8
1.1.2 End-effector type upper-limb rehabilitation robots state of the art
Table 1.1 End-effector type upper-limb rehabilitation state-of-the-art robots
Robot DOF Institute Year of studied
publication
MIT-MANUS 2 Massachusetts Institute of Technology 2003
iPAM 3 University of Leeds 2007
MIME 3 VA Palo Alto and Stanford University 2004
GENTLE/s 3 University of Reading 2003
Among some of the end-effector based devices for rehabilitation we can mention: The MIT-
MANUS, a 2DOF planar robot to provide physical rehabilitation with extremely low inertia
and friction that has presented successful results in tests at the Burke Rehabilitation Hospital
(Krebs et al., 2003). The iPAM robotic system, it uses two manipulator-like robots aimed to
provide assistive upper-limb therapeutic exercises for post-stroke patients. It has a total of
6DOF and holds patient’s arm at that upper arm and forearm level (Jackson et al., 2007). The
MIME system; in it, a robot manipulator (PUMA-560) applies forces to the patient that
would normally be provided by a therapist. It restricts hand and wrist movement and the
focus of the rehabilitation task is aimed to the forearm using goal-oriented movements. It has
also been tested to prove the efficiency of robotic rehabilitation in post-stroke hemiparesis
(Lum et al., 2002; Lum, Burgar and Shor, 2004). The GENTLE/s system, it utilizes an active
3DOF haptic master robot attached to the wrist of the patient. It uses tele-presence and virtual
reality as the method to provide rehabilitation. This approach encourages the patients to
exercise for longer periods of time; it has been tested with stroke patients (Coote et al., 2008;
Loureiro et al., 2003). A very important characteristic of this type of robotic devices is that
they do not actively support the extremity. Table 1.1 lists the systems described above.
9
1.1.3 Exoskeleton type upper-limb rehabilitation state of the art robots
Table 1.2 Exoskeleton type upper-limb rehabilitation state-of-the-art robots
Robot DOF Institute Year of studied publication
ETS-MARSE 7 École de technologie supérieure 2015
CADEN-7 7 University of Washington 2007
ABLE 4 Interactive Robotics
Unit of CEA-LIST 2010
SARCOS 7 University of Southern California 2005
Between some of the exoskeletons devices for rehabilitation we can mention: ETS-MARSE,
our project, a 7DOF manipulator-like exoskeleton (Rahman et al., 2015b). It has been
developed to the point of having passive, active-assisted and active rehabilitation routines. It
remains pending to improve security protocols for the human-machine interaction and to
initiate tests with patients to validate the effectiveness of such schemes to provide
rehabilitation. The CADEN-7 (Perry, Rosen and Burns, 2007), a 7DOF exoskeleton currently
in the third generation of this project. It is controlled by two PCs, one for the low level
control (servo control) and the other that calculates the force feedbacks that need to be
rendered and applied by the exoskeleton arm, retrieving information from three multi-axis
force/torque sensors and can run the virtual environment to be simulated to the user. It can
perform different tasks, under four modalities: active and passive mode of rehabilitation,
assistive device, haptic device and master device. The ABLE robot, an anthropomorphic
upper limb exoskeleton which innovative actuators design allows it to be highly reversible
(Garrec, 2010). The 4DOF version was being tested for rehabilitation proposes and the
design to create a forearm-wrist module with the remaining 3DOF was under development.
The Sarcos Master Arm system (Mistry, Mohajerian and Schaal, 2005), a 7DOF hydraulic
model. Besides rehabilitation, it is used to model and study issues of motor control in the
human arm by applying forces in the joints as perturbations to learn about the human use of
arm redundancy to adapt to this constrains. Table 1.2 lists the systems described above.
10
1.1.4 Limitations of current approaches
Besides the extensive research and great progress in the field of upper-limb robotic
rehabilitation, we still can mention a list of limitations that encompass both hardware design
and control algorithms. As the main hardware limitations, we can mention:
Limited degrees of freedom;
Limited range of motion with respect to human range of motion;
Complex and robust structures;
Big-sized joint actuators;
Weak joint mechanisms;
Inadequate or not-present safety measurements;
Lack of adequate gravity compensation;
Complex coupling mechanisms for arm attachment;
Use of wires with intricate routing mechanisms for power transmission.
As the main limitations in control approaches we can mention:
Use of linear control techniques as PD and PID;
Very heavy computational demands to handle very complex dynamic models;
Use of simplified models that can introduce lack of robustness and decrease tracking
performance;
Chattering when Sliding Mode Control is used.
1.2 Research objectives and methodology
The global objective of this project is to obtain an arm orthosis that can offer passive, active-
assistive and active rehabilitation to physically disable people, with full shoulder, elbow and
wrist rehabilitation capabilities. To achieve this main objective the ETS-MARSE exoskeleton
was used, developed in its mechanical part and first control approaches in a preceding
research work of our research group (Rahman, 2012). The focus of the work described in this
thesis is to apply a suitable control algorithm for the robot positioning and to develop a
sensing interface between the human and the robot that can provide the control of the
11
exoskeleton by direct command from the person; i.e., to capture the intension of movement
of the user to provide active-assisted and active rehabilitation. To that purpose, the following
specific objectives with the described methodology were applied during this research project:
1.2.1 Development of the nonlinear control law
Different control techniques were studied. Because the nonlinear nature of the kinematic
chain model of a human arm, the resultant model is nonlinear. Nevertheless, approaches as
regular and enhanced PID were studied as well as the most used nonlinear control techniques
as computed torque control and sliding mode control. A relatively new technique was
implemented: Virtual Decomposition Control. A direct comparison between VDC, CTC and
SMC was done. Because its advantages, already described, VDC is now used as the main
nonlinear control law of the ETS-MARSE.
1.2.2 The sensing interface
This objective involved the analysis, study and implementation of the human-machine
interface to obtain the motion intention for the active-assisted and active rehabilitation
modes. Force control was implemented by means of the virtual work principle transformation
and an admittance function. As the input to the controller, a force sensor was used as well as
a nonlinear perturbation observer. Studies in the area of EMG signals were started and the
first result towards control directed by means of these signals were implemented and
presented. Teleoperation was begun to be studied.
1.2.3 Inverse Kinematics
In order to perform rehabilitation tasks, some trajectories must be provided in Cartesian
space. Although the redundancy problem was not solved, an approach to manage some
Cartesian trajectories through the Jacobian pseudo-inverse technique was implemented.
12
1.2.4 Implementation and experimentation
Besides design and simulation with a variety of tools (MATLAB, Mathematica, and
LabVIEW), all the control techniques and methods studied in this research work were
implemented on the ETS-MARSE.
To summarize the structure of the present work, Figure 1.1 condenses the methodology
described above.
Figure 1.1 Methodology
1.3 Originality of the research and contribution
Besides that in this area extensive studies, models, and projects have been done, still remain
in front many options to improve and contribute to this technology as well as many problems
and areas of opportunity that need to be solved. Particularly, completely satisfactory results
that offer passive, active-assisted an active rehabilitation to the 7DOF of the human arm are
13
not available yet commercially. One of the important contributions of this work is that our
robot covers the main seven degrees-of-freedom of the human arm and it presents passive,
active-assisted and active rehabilitation schemes. In the particular case of the control, the
integration to the ETS-MARSE of the Virtual Decomposition Control, a relatively new
approach that showed advantages over other classic techniques, is an important aspect of this
research.
In general, the results contribute in an area of constant growth, permitting to complement the
existing knowledge in the field. Finally, the most important contribution will be to help
people with physical disability to assist the rehabilitation process, helping them to return to a
productive and more independent life, improving in a significant way its quality of life.
CHAPTER 2
VIRTUAL DECOMPOSITION CONTROL OF AN EXOSKELETON ROBOT ARM
Cristóbal Ochoa Luna1, Mohammad Habibur Rahman1, 2, Maarouf Saad1, Philippe
Archambault2, 3, and Wen-Hong Zhu4 1Department of Electrical Engineering, École de technologie supérieure,
1100 Notre-Dame West, Montreal, Quebec (H3C 1K3) Canada. 2School of Physical & Occupational Therapy, McGill University,
3654 Prom Sir-William-Osler, Montréal, Québec (H3G 1Y5) Canada. 3Centre for Interdisciplinary Research in Rehabilitation (CRIR),
2275 Laurier Avenue East, Montréal, Quebec (H2H 2N8) Canada. 4Space Exploration, Canadian Space Agency,
6767 Route de l'Aéroport, Longueuil (St-Hubert), Quebec (J3Y 8Y9) Canada.
This paper was published in Robotica on October 14, 2014
Abstract:
Exoskeleton robots, which can be worn on human limbs to improve or to rehabilitate their
function, are currently of great importance. When these robots are used in rehabilitation, one
aspect that must be fulfilled is their capacity to adapt to different patients without
significantly varying their performance. This paper describes the application of a relatively
new control technique called Virtual Decomposition Control (VDC) to a seven degrees-of-
freedom (DOF) exoskeleton robot arm, named ETS-MARSE. The VDC approach mainly
involves decomposing complex systems into subsystems, and using the resulting simpler
dynamics to conduct control computation, while strictly ensuring global stability and having
the subsystem dynamics interactions rigorously managed and maintained by means of virtual
power flow. This approach is used to deal with different masses, joint stiffness and
biomechanical variations of diverse subjects, allowing the control technique to naturally
adapt to the variances involved and to maintain a successful control task. The results
16
obtained in real time on a 7DOF exoskeleton robot arm show the effectiveness of the
approach.
Keywords: Exoskeleton robot, Virtual Decomposition Control, passive rehabilitation, active
rehabilitation, upper-limb impairment, dynamic variations.
2.1 Introduction
Orthotic robots, or exoskeletons, mimic and adapt to the structure of an injured limb to
improve, re-establish or complete some of its functionality (Pons, 2008). Following
occupational and sport injuries, traumas, geriatric disorders (Department of Economic and
Social Affairs, 2013) and strokes (Mackay and Mensah, 2004), etc., diverse types of
physiological complications can arise, possibly leading to social, labour and personal
limitations, and consequently decreasing the quality of life of a large number of individuals.
One of the symptoms most often diagnosed as a result of a stroke is the loss of function on
one side of the body. The main treatment for this is rehabilitation, which requires hours of
highly skilled and extensive procedures. The number of people qualified to provide such
support is hardly enough to treat all patients affected. Rehabilitation can be supplemented
with the use of robots, especially wearable (orthotic or prosthetic) robots (Garrec et al., 2008;
Nef et al., 2009; Rahman et al., 2012c). These robots can help people by reducing the
impacts of their disabilities and by significantly improving their quality of life.
Passive arm movement therapy is a form of treatment used among patients who are unable to
actively move their arms throughout their complete range of motion, following a
neurological insult, such as a stroke, which can lead to weakness or paralysis. In passive
rehabilitation, the affected limb is moved by external forces (therapist or robot) while the
patient relaxes. Active rehabilitation for its part focuses on long-term results; it encourages
subjects to move their arms by themselves in order to build muscle strength and flexibility.
These issues must therefore be properly addressed in rehabilitation robotics. In the area of
upper limb rehabilitation, which was initialized in the middle of the twentieth century (Van
17
der Loos and Reinkensmeyer, 2008), it was not until very recently that truly functional
experimental implementations were obtained with the full capabilities of the whole arm
(shoulder, elbow and wrist) (Perry and Rosen, 2006; Tsagarakis, Caldwell and Medrano-
Cerda, 1999). Different studies have shown that the use of robotic tools in rehabilitation
provides intensive therapy that leads to measurable functional gains (Eschweiler et al., 2014;
Lo and Xie, 2012; Norouzi-Gheidari, Archambault and Fung, 2012; Sarakoglou et al., 2007).
To that end, work in our laboratory has led to the development of a seven DOF exoskeleton
robot to ultimately assist patients with shoulder (3DOF), elbow (1DOF), and wrist (3DOF)
movements (Rahman et al., 2015b). The primary objective of this research is to develop a
robotic device that can offer passive and active rehabilitation, as well as daily assistance of
the upper limbs, to physically disabled people.
A wide range of approaches have been proposed to control rehabilitation robots, ranging
from simple PD controllers to nonlinear techniques such as Computed Torque Control (CTC)
and Neuro-Fuzzy controllers. Some attractive combined approaches, such as an adaptive
Fuzzy controller based on Sliding Mode Control (SMC), for example, was presented by Sun
et al (Sun, Sun and Feng, 1999), and seems to be able to deal with the inherent chattering of
the SMC, subject to model uncertainties and external disturbances. A combination of
adaptive and robust control (Uzmay and Burkan, 2002) merges the advantages of both
control laws, eliminating the disadvantage of adaptive controllers in transient behaviour and
suppressing the steady-state error. Furthermore, a CTC with Fuzzy Control (Song et al.,
2005) provides satisfactory results, subject to manipulator-structured and unstructured
uncertainties. An adaptive control with an Artificial Neural Network was presented by Ciliz
(Ciliz, 2005) for dealing with frictional uncertainties, which are highly difficult to model.
Some other approaches use robust adaptive control that indicate an interesting way of dealing
with system uncertainties and external disturbances (Li et al., 2008; Zhijun et al., 2008).
However, some fundamental problems are yet to be solved.
In CTC, the main concern is that the control only shows moderate performance improvement
when the dynamical model is not exactly known, and this is true even for robots with
18
relatively small numbers of DOF, such as 4DOF orthosis (Brackbill et al., 2009) for example.
Neuro-fuzzy controllers are highly complex, and use different sets of rules and layers
involving switching in different regions of operation. This is true even for 3DOF arm
exoskeletons (Rahman et al., 2006). In most of the above-mentioned approaches (Ciliz, 2005;
Li et al., 2008; Song et al., 2005; Sun, Sun and Feng, 1999; Uzmay and Burkan, 2002; Zhijun
et al., 2008), the results are mainly restricted to simulations (i.e., a 2DOF manipulator (Sun,
Sun and Feng, 1999), a two-link planar robot (Uzmay and Burkan, 2002) and a two-link
elbow planar manipulator (Song et al., 2005)) or implementation on simple robots (i.e.,
successfully tested on a two-link SCARA type direct drive arm (Ciliz, 2005)).
As can be seen, two specific problems need to be considered together in exoskeleton
research: the high number of degrees-of-freedom and the system variability (biomechanical
and physiological). For these reasons, a novel application of the Virtual Decomposition
Control (VDC) technique is introduced in this paper for the control of exoskeleton robots, in
order to address two important issues: a) to facilitate the implementation of a high degree-of-
freedom robot (7DOF in this case), and b) to cope with the changes in the dynamics of the
robot-human system, due to the biomechanical and physiological characteristics of different
patients. As robots become more complex, the complexity of the control task increases as
well. Indeed, the complexity of the computation of robot dynamics is proportional to the
fourth power of the number of degrees-of-freedom in Lagrangian dynamics (Zhu, Piedboeuf
and Gonthier, 2006). This research deals with a complex 7DOF robot. The VDC approach
allows us to break the system down into subsystems with relatively simpler dynamics and to
apply the control directly over those subsystems. The Virtual Decomposition Control uses
the dynamics of subsystems (rigid links and joints) to conduct control design, while
rigorously maintaining the L2 and L∞ stability of the entire robotic system (Zhu and De
Schutter, 2002). This virtual decomposition yields simpler dynamic equations, both in their
formulation and implementation. Proceeding as such maintains the complexity of the
dynamics of the subsystems constant, meaning that as more and more DOF are added to the
robot, the complexity of the total system increases linearly. With the system broken down
into simpler subsystems, the VDC handles the dynamic interactions among subsystems
19
mathematically through the definition of virtual power flows. Thus, even with the subsystem
decomposition, the highly nonlinear dynamics of the robotic system are not decoupled,
thereby maintaining the control and stability of the entire system.
An additional advantage of the VDC is its ability to manage, through its parameter
adaptation, the inherent variability that is present in human dynamics. In addition to the
imperfect knowledge of the dynamics of the body structures, different individuals will
display differences in body mass, weight distribution, limb length, etc. Moreover, muscular
and neurological conditions can change the visco-elastic properties of muscles and joints. For
controllers that need to know the dynamical model of the system (e.g., CTC), variations in all
these parameters could have a negative impact on the performance of the robot. In our
previous research (Rahman et al., 2012b), SMC was implemented for dynamic trajectory
tracking corresponding to typical passive rehabilitation exercises. Though SMC performed
well, it also showed some limitations in dealing with different subjects. The adaptive
characteristics of the VDC overcome this limitation by dealing with biomechanical and
physiological variations, providing a better and constant performance of the exercises.
The original contribution of this paper is the application of the VDC to address the issue of
dynamic variability, due to individual differences, in order to obtain constant performance by
a rehabilitation exoskeleton arm. As well, the simplification of the control task of these
multi-articulated robots, through the virtual decomposition process and the use of virtual
stability and virtual power flows, allows a simpler computation for systems with high
numbers of degrees-of-freedom. The experiments were carried out on different healthy
subjects with the ETS-MARSE exoskeleton robot, designed by our research team.
This paper is organized as follows: section 2.2 presents a brief description of the robot and its
characteristics. Section 2.3 lays out a detailed presentation of the control development.
Finally, in section 2.4, the implementation of the control and experiments executed are
explained and the results are presented and discussed, followed in section 2.5 by the
conclusions of the work.
20
2.2 Characteristics of the Motion Assistive Robotic Exoskeleton for Superior Extremity
The wearable upper-limb exoskeleton robot, named “Motion Assistive Robotic Exoskeleton
for Superior Extremity” (ETS-MARSE) has 7DOF, and was designed to correspond to the
natural range of movement of the upper extremity of the human body. It is comprised of a
shoulder motion support part (which assists in horizontal flexion/extension (Figure 2.1a),
vertical flexion/extension (Figure 2.1b), and internal/external rotation (Figure 2.1c) of the
shoulder), an elbow motion support part (Figure 2.1d) for elbow flexion/extension, a forearm
motion support part which is responsible for forearm pronation/supination (Figure 2.1e), and
a wrist motion support part (for flexion/extension (Figure 2.1f) and radial/ulnar deviation
(Figure 2.1g) of the wrist).
Figure 2.1 Joint range of motion of ETS-MARSE
(a) shoulder joint: horizontal flexion/extension; (b) shoulder joint: vertical flexion/extension; (c) shoulder joint: internal/external rotation; (d) elbow flexion/extension; (e) forearm pronation/supination; (f) wrist
21
The exoskeleton is an open kinematic chain, manipulator-like robot, with seven revolute
DOF( = 7). The kinematics of any robot can be described with four parameters per joint,
two describing the joint, and two for its connection with the adjacent joint. One parameter is
the joint variable (angle if revolute, distance if prismatic), while the other three are constants
(an angle or a distance, opposite of the joint variable and the angle and distance from joint to
joint). This convention is known as the Denavit-Hartenberg notation; it has two variations,
the original and the modified. As described in Craig (Craig, 2005), with the frames attached
to the robot as shown in Figure 2.2, the modified Denavit-Hartenberg parameters are
obtained and summarized in Table 2.1.
Figure 2.2 7DOF Exoskeleton robot arm
Frame {0} represents the base frame; frame {1}: shoulder horizontal flexion/extension; frame {2}: shoulder vertical flexion/extension; frame {3}: shoulder internal/external rotation; frame {4}: elbow flexion/extension; frame {5}: forearm pronation/supination; frame {6}: wrist flexion/extension and frame {7}: wrist radial/ulnar deviation. Axes shown are in positive direction
22
Table 2.1 ETS-MARSE Modified Denavit-HartenbergParameters
i αi-1 ai-1 di θi
1 0° 0 d1 θ1
2 -90° 0 0 θ2
3 90° 0 d2 θ3
4 -90° 0 0 θ4
5 90° 0 d5 θ5
6 -90° 0 0 θ6-90°
7 -90° 0 0 θ7
2.3 Analysis of the ETS-MARSE robot with Virtual Decomposition Control (Zhu et al., 1997)
The first step in VDC analysis is to perform the virtual decomposition of the robot; in this
case, the exoskeleton is a single open chain. This decomposition allows us to base control
directly on subsystem dynamics, allowing it to remain relatively simple, i.e., proportional to
the number of subsystems. Decomposition is done by placing virtual cutting points
separating each joint and link of the system into a subsystem. Although the robot or the
human arm does not have seven links (see Figure 2.2), this is a virtual decomposition, and is
performed as such to express the system in its most basic operative units. This is a basic
approach of VDC to maintain the equations of the system at their most simple expressions
for computational handling; another advantage is that if a change is made to any actuator,
only the dynamics of that joint will change, not the rest of the system. The result of the
system decomposition is illustrated in Figure 2.3: it yielded a decomposition into fourteen
subsystems, with the virtual cutting points represented by vertical dotted lines, linked to their
respective frames by horizontal dotted lines.
23
Figure 2.3 Virtual decomposition into 14 subsystems
2.3.1 Kinematics
From the resulting modified Denavit-Hartenberg parameters for the decomposition shown in
Figure 2.3, the homogeneous transform matrices of the system are obtained. Using them, it is
necessary to calculate the force/moment transformation matrices between any consecutive { } frames for = 1,… , 6 (see Figure 2.3) as follows:
= ×( ×) ∈ ℝ × (2.1)
where represents the rotation matrix from frame to frame and the
vector pointing from to frame , and:
24
( ×) = 0 − (3) (2) (3) 0 − (1)− (2) (1) 0
(2.2)
where ( ) represents the th term of the vector.
The next step is to calculate , the linear/angular velocity vectors of the { } frames for = 1,… ,7 as follows:
= ∈ ℝ (2.3)
where is the linear velocity vector and is the angular velocity vector of the
corresponding frame. Defining each joint position (angle) as to and using the previous
linear/angular velocity vectors in (2.3), the augmented velocity vector is formed as follows:
= [ ⋯ ⋯ ] (2.4)
Factorizing the joint velocity vector = [ ⋯ ] in (2.4), we obtain:
= (2.5)
where is the VDC Jacobian matrix of the system:
= 0 ⋯ 0 ⋱ ⋮⋮ ⋱ ⋱ 0 …
(2.6)
25
where = [0 0 0 0 0 1] , represents the 7× 7 identity matrix and 0 is a six-
element zero vector. Note that the dimension of is 49 × 7; the aforementioned identity
matrix and a block of 6 × 7 for each one of the seven degrees-of-freedom of the robot.
Finally, for the kinematics, it is necessary to calculate the required velocities, which are
functions of the control requirements. They incorporate terms that allow the tracking of a
control objective to the desired velocities obtained from the trajectory generator. In this case,
position control is used such that the position is incorporated into the vector of required
velocities.
= + ( − ) (2.7)
where = [ ⋯ ] is a 7 × 1 reference velocity vector, = [ ⋯ ] is
the 7 × 1 desired velocity vector, > 0 is a control parameter, = [ ⋯ ] is the 7 × 1 desired position vector and = [ ⋯ ] the 7 × 1 position vector. From (2.6)
and (2.7), the 49 × 1 augmented required velocity vector is obtained as follows:
= (2.8)
From (2.4), it can be established that:
= [ ⋯ ⋯ ] (2.9)
2.3.2 Dynamics
For the simulation, the dynamics of the robot was obtained using the Newton-Euler approach
(Craig, 2005). To apply the VDC approach and to obtain the inverse dynamics that takes part
in the control of the robot, it was necessary to calculate the required force/moment vectors
for the links, , and then the net torques required by the joints, ∗ .
26
From the general formulation of a rigid body dynamics, in which one frame { } is used as
the reference to express the dynamics, and another frame { } is assumed to be located at the
centre of mass, the rigid body dynamics can be expressed as:
( ) + ( ) + = ∗ (2.10)
where (Zhu et al., 1997):
= − ( ×)( ×) − ( ×) (2.11)
( )= ( ×) − ( ×)( ×)( ×)( ×) ( ×) + ( ×) − ( ×)( ×)( ×)
(2.12)
= ( ×) (2.13)
where ∈ ℝ is the mass of the rigid body, is a 3 × 3 identity
matrix, = ( ) is time invariant, ( ) ∈ ℝ × denotes the moment of inertia
matrix around the centre of mass, ∈ ℝ × is the rotation matrix from frame to the
inertial frame, r ∈ ℝ is the vector pointing from frame to frame , ∈ ℝ is the
angular velocity vector, = [0 0 9.81] ∈ ℝ and ( ×) and ( ×) are defined as
in relation (2.2).
Substituting from (2.10) the dynamic model velocity vector by the required velocity
vector ∈ ℝ defined in (2.9), the following equation is defined:
( ) + ( ) + ≝ (2.14)
27
where ∈ ℝ × is a regressor matrix composed of elements of / ( ) ∈ ℝ , the
velocity vectors ∈ ℝ and ∈ ℝ and terms from the vector of gravity propagation,
and ∈ ℝ is the vector composed of the mass of the link, the elements of the vector
pointing from the origin of the reference frame of the link toward its mass centre, and
elements of the inertia tensor of the body. The exact representation of each element of and
is given in Appendix A.
By means of the linear parameterization expressed above in (2.14), the first step for the link
dynamics is to obtain the required net force/moment vectors with the following equation:
∗ = + ( − ) (2.15)
for = 1,… ,7 where ∗ are the required net force/moment vectors, is a symmetric
positive-definite gain matrix, and are the velocities defined in (2.4) and (2.9), and ∈ ℝ is the estimated parameter vector. The estimation of the parameters in is defined
as follows (Zhu et al., 2013):
= ( ), , ( ), ( ), (2.16)
for = 1,… ,7 and = 1,… ,13,where represents the th parameter of the th link, ( ) ∈ ℝ is a scalar variable defined as the th element in:
= ( − ) (2.17)
is the parameter update gain, ( ) and ( ) are the lower and upper bounds of
respectively, and the projection function is a differentiable scalar function (Zhu and De
Schutter, 1999) defined for ≥ 0 such that its time derivative is governed by:
= ( ) (2.18)
28
with:
= 001 ≤ ( ) ( ) ≤ 0 ≥ ( ) ( ) ≥ 0ℎ
Once this step is complete, the required force/moment vectors at the cutting points are
obtained as follows:
= ∗ = ∗ +
(2.19)
for = 6,… ,1. The next step is the calculation of the dynamics of the joints. For = 1,… ,7
in (2.20) to (2.24), the following vector and parameter vector are defined:
= [ ( ) 1] (2.20)
= [ ] (2.21)
where the sub-index in the vectors is used to differentiate joint variables from the link
variables introduced in (2.15), is the equivalent mass or moment of inertia, > 0
denotes the Coulomb friction coefficient, > 0 is the viscous friction coefficient and
denotes an offset that accommodates asymmetric Coulomb frictions. The adaptation of the
parameters defined in (2.21) is calculated as:
= ( ), , ( ), ( ), (2.22)
for = 1,… ,7 and = 1,… ,4,where represents the th parameter of the th joint, ( ) ∈ ℝ is a scalar variable defined as the th element in:
= ( − ) (2.23)
29
is the parameter update gain, ( ) and ( ) are the lower and upper bounds of
respectively, and the projection function is a differentiable scalar function defined in
(2.18).
Finally, the net torque for the joint ∗ is obtained as follows:
∗ = + ( − ) (2.24)
where ∗ is the net torque of the joint, denotes a feedback gain and ∈ ℝ defined in
(2.22) denotes the estimate of ∈ ℝ defined in (2.21).
2.3.3 Control
To develop the control of the entire system, the torques resulting from the link and joint
analysis are combined. First, it is necessary to extract the torque of the link force/moment
vector as follows:
= (2.25)
for = 1,… ,7. With = [0 0 0 0 0 1] that was defined earlier, the control torque
is designed as:
= ∗ + (2.26)
for = 1,… ,7. The flow diagram with the calculations needed in the VDC technique is
shown in Figure 2.4.
30
Figure 2.4 Block diagram of the system (with the equations used in each step in the parentheses)
Associating (2.26) with the traditional dynamic equation of a manipulator:
= ( ) + , + ( ) + ( , ) (2.27)
where ( ) is the manipulator’s × mass matrix, , the × 1 Coriolis and
centrifugal terms vector, ( ) the × 1 gravity terms vector and ( , ) the × 1 torque
friction vector. It is clear that in the case of VDC, the parameter adaptation that is defined in
(2.15) and (2.24) from equations (2.10) to (2.14) for the rigid links and (2.20) to (2.21) for
the joints, will incorporate not only the mass, inertia (moments and products) and centre of
mass parameters of the links, and the moment of inertia and friction for the joints of the
robot, but also the uncertainties and the disturbances introduced by the subject, which are not
modelled. For example, the mass of the human arm (different from subject to subject) will be
combined with the links’ mass; changes or displacements in the position of the arm of the
subject, combined with changes in position of the centre of mass; and friction of the joints,
combined with constraints of the movement caused by the subject’s limitations, such as
difficulty to move due to spasticity or altered muscle tone.
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2.3.4 Stability Analysis
Given the dynamics expressed in relation (2.27) and the control design given in (2.19) and
(2.24), combined as indicated in (2.25) and (2.26), the asymptotic stability is ensured if the
position and velocity errors converge asymptotically to zero:
→ ‖ ( ) − ( )‖ → 0 (2.28)
→ ‖ ( ) − ( )‖ → 0 (2.29)
with q and q vectors defined in (2.4) and (2.5) and and vectors defined in (2.7).
Using the Lyapunov approach, a non-negative candidate function is defined and then it is
shown that the variation is a decreasing function. As explained in the previous section, the
system dynamics has two parts. The first represents the link dynamics given by:
+ + = ∗ = 1… (2.30)
And the second, given in relation (2.31), represents the joint dynamics, characterized by the
torque resultant from the moment of inertia plus the torque from the Coulomb friction:
+ ( ) = ∗ = 1… (2.31)
Therefore, considering the Lyapunov candidate function for the entire robot as:
= + (2.32)
where represents the non-negative Lyapunov candidate function related to the link
dynamics and is the non-negative Lyapunov candidate function related to the joint
32
dynamics. Combined with the control equation (2.15) and the parameter adaptation defined
in (2.16) and (2.17), is defined as follows:
= 12 − − + 12 ( − )
(2.33)
The non-negative Lyapunov candidate function related to can be defined as follows:
= 12 ( − ) + 12 ( − )
(2.34)
The derivative of the Lyapunov candidate function (2.32) is given as:
= + (2.35)
Before showing that relation (2.35) is always decreasing, it is necessary to define the virtual
power flows as the inner product of the linear/angular velocity vector error and the
force/moment vector error (Zhu and Lamarche, 2007; Zhu et al., 1997). With respect to a
frame A:
≝ ( − ) ( − ) (2.36)
virtual power flows characterize the dynamic interaction between subsystems at its cutting
points. They are analogue to power flows within a rigid body, but instead of being the inner
product of a velocity vector and a force vector, they are the inner product of a velocity vector
error and a force vector error. With definition (2.36), it follows that:
≤ − − − + − ∗ − ∗ (2.37)
33
Considering (2.36) and the force/moment transformation matrices defined in (2.1) to
transform the velocities expressed in (2.3) and the required velocities expressed in (2.9), and
with the net force/moment and required net force/moment vectors (2.19), this yields:
− ∗ − ∗ = − (2.38)
where the terms on the right side of (2.38) represent the virtual power flows at the two
cutting points of each link.
can be written (Zhu et al., 1997) as:
≤ − ( − ) − + (2.39)
Considering an open chain structure, as is the case in this paper, and with = 0 and = 0, the total virtual power flows gives:
− = 0 (2.40)
Therefore, relationship (2.37) becomes:
≤ − − − (2.41)
and the function becomes:
≤ − ( − ) (2.42)
Finally, from relationships (2.41) and (2.42), and given positive gains and , the
derivative of the Lyapunov function , given in (2.43), is always decreasing.
34
≤ − ( − − + ( − ) ) (2.43)
The asymptotic stability in the sense of Lyapunov follows immediately from the bounded
reference signals, the bounded control and the bounded joint acceleration.
2.4 Experimental Results
A general overview of the ETS-MARSE robot is shown in Figure 2.5. Brushless DC motors
(Maxon EC-45, EC-90) incorporated with harmonic drives (having gear ratio 120:1 for motor
1 and motor 2, and gear ratio 100:1 for motor 3 to motor 7) were used to actuate the ETS-
MARSE.
Figure 2.5 ETS-MARSE with human subject
A block diagram of the experimental setup, including the control architecture, for the ETS-
MARSE system is depicted in Figure 2.6. For the experimental phase, three control
techniques were used: VDC as the focus of this research and CTC and PID as reference
control strategies. The outputs of the controllers were the joints’ torque commands. However,
the torque commands were converted to motor currents, and finally, to reference voltages as
35
voltage value is the drive command for the motor drivers. The implementation of the system
was carried out in a National Instruments PXI system. A PXI-8108 controller card performed
the joint-based control (VDC, CTC and PID) and served as the robot operating system. A
FPGA (Field Programmable Gate Array) mounted in the NI PXI-7813R remote input-output
card, performed the low-level (PI) control, that is, the current loop for the robot actuators and
the position feedback control via Hall sensors. The sampling rate for the VDC controller was
1ms and 500µs for the CTC and PID (Figure 2.6, left dotted box). Note that the current loop
controller has a sampling time of 50µs (up to 20 times faster) than the torque control loop
(Figure 2.6, right dotted box). Also, a host computer was used (not shown in the schematic of
Figure 2.6), which displayed the user interface through which it connected to the ETS-
MARSE system in order to issue commands (such as selection of exercise or control
techniques) to the PXI, and to provide feedback and retrieve experimental data from the
system for analysis, as well as the virtual environment used in active rehabilitation.
Figure 2.6 Experimental setup with control architecture
2.4.1 Varying subjects experiment
In these experiments, the variation of the trajectory tracking performance of the ETS-MARSE
was evaluated. The experiment was divided into three scenarios: one with the VDC, another
with the PID, and the last with the CTC. Although the CTC controller can include a simple
PID controller for the decoupling and cancelation of nonlinear terms, in this case CTC was
used with a PD controller. The PID controller described in these tests is different; as a
36
traditional PID controller, it attempts to minimize the position error through the adjustment
of the torque without any need for dynamic modelling of the robot, and only some tuning of
the gains is performed. For the CTC controller (with its internal PD), a complete modelling
of the robot’s dynamics should be done. The trajectory used in this research represents a
typical passive rehabilitation exercise (Brigham and Women’s Hospital Rehabilitation
Services, 2014). It is a joint space trajectory, an outside reaching movement, illustrated in
Figure 2.7, and involving the shoulder, elbow and forearm motion: in each exercise, the robot
followed the path from A to B (in four seconds) and then reversed direction from B to A
(also in four seconds) three times.
Figure 2.7 Schematic diagram, reaching movement exercise
The range of motion of each joint is summarized in Table 2.2; since the wrist is not moved in
this experiment (joint 6 and joint 7), only joint 1 to joint 5 are presented. To introduce the
system variability, this exercise was executed with four different situations: three healthy
male human subjects (ages: 24, 33 and 31 years; height: 181, 165 and 182 cm; weight: 75, 63
and 95 Kg) and one scenario without a subject. Experiments with subjects were conducted
with them in the seated position, analogous to Figure 2.5. A height-adjustable chair was used
to adjust the seating height, i.e., to align the centre of rotation of the shoulder joint of the
subject to that of the ETS-MARSE.
37
Table 2.2 Varying subjects experiment range of motion
Joint Type of motion ETS-MARSE
Workspace
Shoulder Joint
Joint 1 Horizontal Flexion 5°
Horizontal Extension 60°
Joint 2 Vertical Flexion 60°
Vertical Extension 0°
Joint 3 Internal Rotation 20°
External Rotation 0°
Elbow
Joint 4 Flexion 90°
Extension 40°
Forearm
Joint 5 Pronation 40°
Supination 0°
It is important to recall that this rehabilitation movement is a passive one; that is, the robot
follows a predefined trajectory with no action from the user. Each condition (i.e., exercises
with subjects A, B and C, and without subject) was repeated seven consecutive times, giving
a total of 28 trials for each controller. It should be mentioned that no changes were made
between the tests, e.g., in terms of gains or parameters in the control strategy.
The experimental results are presented in Figure 2.8. Each plot corresponds to one control
strategy, and each one shows the RMS value of the trajectory tracking error for each joint
moved, along the 28 tests. It should be recalled that even when all joints are involved in the
control, joint 6 and joint 7 of the ETS-MARSE remained at zero degrees, and so were not
analysed. It is clear that, in addition to providing a lower tracking error, the VDC controller
remained barely affected by variations. Meanwhile, the PID controller presented a more
38
variable behaviour, and the CTC was the most affected by changes in the subject’s
characteristics.
Figure 2.8 RMS joint tracking error along the 28 tests for each controller
The three controllers performed well, but the analysis that is pertinent for this paper is the
variation in the performance from one experiment to another due the dynamic variations. In
Figure 2.9, the average RMS error (joint 1 to joint 5) of each test and for each controller is
shown. It can easily be seen how the VDC results are the more compact, confirming that the
controller behaves better over distinct dynamic conditions caused by changes of test subjects.
It should be noted that the changes from one condition to the other are also present in the
VDC, but the variation is small compared to the other techniques used in this paper. It is also
clearly seen that the other controllers changed their behaviour notably even under the same
testing condition, that is, with the same subject (or without subject), possibly due to natural,
unintended changes in the arm position, relaxation, grip on the handle, etc.
39
Figure 2.9 Average (joint 1 to joint 5) RMS error of each test
Table 2.3 Statistical analysis of performance variation
Controller RMS Error σ(°) Average RMS
Error σ(°)
Normalize to VDC
RMS Error σ Joint 1 Joint 2 Joint 3 Joint 4 Joint 5
VDC 0.0180 0.0251 0.0243 0.0330 0.0086 0.0218 1.00
PID 0.0703 0.1116 0.1314 0.0483 0.0187 0.0761 3.49
CTC 0.2887 0.0455 0.6731 0.0789 0.0552 0.2283 10.47
Finally, in order to provide a quantitative analysis, Table 2.3 summarizes the standard
deviation (σ) of the data plotted in Figure 2.8 and Figure 2.9. The second to the sixth
columns represent the standard deviation of the RMS error for each joint (Figure 2.8). The
seventh column is the standard deviation of the average RMS error across joints one to five
(Figure 2.9). For a better comparison, the average RMS error was normalized to that of the
VDC in the last column. The PID showed an average RMS error standard deviation more
than three times larger than the VDC; and for the CTC, this was more than 10 times. It can
clearly be seen that a controller that depends heavily on the dynamic model of the system
40
(CTC) is significantly affected by changes and uncertainties caused by the variations in the
robot’s user.
2.4.2 Varying velocity experiment
Another important concern in rehabilitation is movement velocity. To show the efficiency of
the VDC approach in dealing with different velocities, an elbow flexion/extension
experiment is shown. The trajectory of joint 4 (elbow joint) passes through 90°, 5°, 115° and
0°. The speed of the movement was increased for each of the three tests performed. In the
first one, the maximum speed was 20.63°/sec, it was 45.20°/sec for the second one, and -
85.71°/sec for the third test (the minus sign indicates the extension movement). The tests
were conducted with no subject wearing the robot. To compare performances, PID and VDC
were used in each test. Figure 2.10 shows the results for the VDC controller, where each
column displays the position, velocity and error for each movement velocity. Figure 2.11
shows the same for the PID controller. To summarize the performance, Table 2.4 shows the
RMS error in each test. It can be seen that the tracking error for the VDC increased by 83%
from the slowest to the fastest movement, while for PID the increase was by 204%.
Table 2.4 RMS error of varying velocity experiments
Maximum speed
(degrees per second)
RMS Error J4 (°)
VDC
RMS Error J4 (°)
PID
20.63 0.3914 0.3695
45.20 0.4719 0.6209
85.71 0.7169 1.1228
41
Figure 2.10 VDC results for different speeds test
Figure 2.11 PID results for different speeds test
42
2.4.3 Active rehabilitation experiment
Next in the experiment, an active rehabilitation test is presented. Through a virtual
environment as the Human Machine Interface (HMI) (Ferrer et al., 2013), the user’s task was
to follow a predefined trajectory, in this case, a straight line to the front and back, that is,
movement on the X-axis (see Figure 2.7). With the use of a six-axis force sensor mounted on
the tip of the robot (refer to Figure 2.2 or Figure 2.5) the trajectory was actively modified by
an admittance function to make the robot follow the user’s movement intentions. The tip of
the robot, the end effector, is in the handle that the user grabs with his hand while wearing
the robot. The test was completed with the VDC controller. Figure 2.12 shows the user
performing the test with a zoom of the virtual interface in the lower right corner. The red line
in the centre represents the path the user should follow; the white sphere represents the user
end effector, and the green line, the actual trajectory followed by the subject. Finally, Figure
2.13 shows the movement in the Cartesian space in the first column, the force readings of the
force sensor in each Cartesian axis in the second column, and the torque readings in the last
column. Thanks to the robustness of the VDC controller described in subsection 2.4.1 and
subsection 2.4.2, the variations in trajectory tracking observed in this active rehabilitation
exercise were only due to the user’s conditions. This will give a more accurate measurement
of the user performance from test to test.
Figure 2.12 Experimental setup for active rehabilitation
43
Figure 2.13 Cartesian trajectory, forces and torques for active rehabilitation
2.4.4 Parameter adaptation
Finally, to illustrate the parameter adaptation process, a simple experiment was performed.
The adaptation process is shown in the parameters of joint 4. The robot was set at an initial
position with all joints as shown in Figure 2.2, except for joint 4, which was set at 90
degrees. All the parameters were then reset to zero and the trajectory commanded to the robot
only affected joint 4. The test was performed without a subject. It stayed for one second at
the initial position, and then moved from 90 degrees to five degrees in two seconds, and
stayed there for another two seconds. The trajectory is shown in Figure 2.14. Next, Figure
2.15 shows the joints parameters adaptation, defined in (2.21), , the equivalent moment of
inertia, , the Coulomb friction coefficient, , the viscous friction coefficient and , an
offset that accommodates asymmetric Coulomb frictions. It should be recalled that in the
VDC, the algorithm guarantees convergence to a certain value that will ensure the fulfilment
of the control premise as well as the stability demonstrated in subsection 2.3.4, but these
values are not necessarily the real values of the model of the robot. Moreover, it is important
to remember that the gain for the parameter adaptation was individually adjusted for each
44
parameter, as defined in (2.22). The plots show how the first adaptation was done from a zero
value to a certain value corresponding to the initial position. From time = 1 s to time = 3 s,
the parameters adapted according to the dynamics variations of the system in motion. Finally,
arriving at another steady position from time = 3 s onwards, the parameters converge to
another value from there to second five.
Figure 2.14 Left: Robot initial position. Right: Joint 4 trajectory
Figure 2.15 Parameter adaptation of joint 4
45
2.4.5 Discussion of experimental results
The controllers can be tuned in an attempt to achieve a better performance (especially in PID
and CTC cases); nevertheless, the tuning process of the gains or changes in the dynamic
model would need to be repeated for each user. In rehabilitation, if the PID and the CTC
were adjusted for one specific user, this procedure should be repeated for new users with
different dynamics (weight, height, neurological condition, etc.). However, this procedure is
not needed with the VDC because it is based on an adaptive algorithm; the adaptation
process is done online without any manual modification of parameters, which constitutes a
big advantage. Making changes to the control system dynamics in controllers like the CTC is
an undesirable and time-consuming task for the therapist. Besides, physiological changes due
to an improvement in the subjects’ condition (such as stiffness) can be another source of
periodical variances (reduced resistance with time). These problems are clearly avoided by
the use of the VDC. Further, in the experiment presented in subsection 2.4.2, it can be seen
that at low velocity, the PID and VDC controllers perform almost equally well. It is crucial to
understand that this reflects proper tuning of the gains. Thus, the variations in the system
dynamics (in this case, movement velocity) are what lead to a worsening of performance for
the PID controller. It should be mentioned that the velocity test was performed without a
subject in a bid to specifically isolate the effects of the variations in movement velocity. The
results from subsection 2.4.1 and subection 2.4.2 should be considered together, thus
supporting the need, in rehabilitation, to have a controller that is robust to changes in
biomechanical and physiological conditions. Finally, the active rehabilitation scenario shows
that in an active exercise, the tracking of the patient’s improvement will be better known,
since the uncertainty caused by the system variation will be considerably reduced by the
VDC controller approach.
2.4.6 Safety
It is very important to mention that the capacity to deal with the characteristics of different
subjects does not mean that regardless of the subjects’ capabilities, the robot will force them
46
to complete the trajectory. The control interface has the provision to modify the position and
the velocity limits of the joints, in order to adapt to the different conditions and rehabilitation
needs of the subjects. The robot also has mechanical stoppers to maintain the maximum
allowable range of motion inside the normal range of human activities of daily living, with
these limits illustrated in Figure 2.1.
2.5 Conclusions and Future Work
Trajectory tracking exercises, representing passive and active rehabilitation therapy, were
implemented using the VDC approach with trajectories given in joint and in Cartesian space
with excellent results. As to their application to rehabilitation, the experimental results show
that VDC can respond to subject variations and can effectively accomplish rehabilitation
therapy. A performance evaluation against CTC and PID, with all controllers using fixed
gains, successfully demonstrated the advantage of the VDC. In experiments, the tracking
performance of the robot was compared for different controllers, while varying the subjects’
physical characteristics or the movement velocity. The results indicate that the robot under
VDC control can better adapt to these variations, as compared to PID and CTC. Thus, we
conclude that with this VDC’s robustness, a more systematic rehabilitation can be
accomplished. The VDC controller will reduce the variation of the trajectory tracking and
will provide a better measure of the patient’s improvement, as the most important source of
variation in movement performance will be the changes in their condition.
A future step in the development of this project is to continue the development of active
rehabilitation, where the robot helps the user in completing a given movement. This includes
active-assistive rehabilitation, in which the robot can help the subject to different degrees,
according to specific rehabilitation needs (time, movement boundaries, etc.). More active
rehabilitation work has been developed in our lab, such as changing the effort required of the
user to move the robot. Still additional active rehabilitation tasks are to be incorporated,
using electromyographic (EMG) signals, to provide the system with another source of
information regarding the user’s intention of movement. These EMG signals can be used as a
47
full rehabilitation scheme or combined with force sensor data in order to offer the adequate
rehabilitation therapy according to patients’ needs. Haptic capabilities are already under
development for the ETS-MARSE.
CHAPTER 3
ADMITTANCE-BASED UPPER LIMB ROBOTIC ACTIVE AND ACTIVE-ASSISTIVE MOVEMENTS
Cristóbal Ochoa Luna1, Mohammad Habibur Rahman1, 2, Maarouf Saad1, Philippe S.
Archambault2, 3 and Steven Bruce Ferrer1 1Department of Electrical Engineering, École de technologie supérieure,
1100 Notre-Dame West, Montreal, Quebec (H3C 1K3) Canada. 2School of Physical & Occupational Therapy, McGill University,
3654 Prom Sir-William-Osler, Montréal, Québec (H3G 1Y5) Canada. 3Centre for Interdisciplinary Research in Rehabilitation (CRIR),
2275 Laurier Avenue East, Montréal, Quebec (H2H 2N8) Canada.
This paper was published in the International Journal of Advanced Robotic Systems on
September 01, 2015
Abstract:
This paper presents two rehabilitation schemes for patients with upper limb impairments. The
first is an active-assistive scheme based on the trajectory tracking of predefined paths in
Cartesian space. In it, the system allows for an adjustable degree of variation with respect to
ideal tracking. The amount of variation is determined through an admittance function that
depends on the opposition forces exerted on the system by the user, due to possible
impairments. The coefficients of the function allow the adjustment of the degree of assistance
the robot will provide in order to complete the target trajectory. The second scheme
corresponds to active movements in a constrained space. Here, the same admittance function
is applied; however, in this case, it is unattached to a predefined trajectory and instead
connected to one generated in real time, according to the user’s intended movements. This
allows the user to move freely with the robot in order to track a given path. The free
movement is bounded through the use of virtual walls that do not allow users to exceed
certain limits. A human-machine interface was developed to guide the robot’s user.
50
Keywords: Upper limb rehabilitation, active and active-assistive rehabilitation, admittance,
7DOF exoskeleton, human-machine interface
3.1 Introduction
Upper extremity paralysis (the inability of a muscle or group of muscles to move voluntarily)
occurs as a consequence of lesions such as injuries to the central or peripheral nervous
system. Causes of injuries include strokes, sports mishaps and car or occupational accidents,
among others. According with the US National Stroke Association®, approximately 80% of
stroke survivors experience hemiparesis, which causes weakness or an inability to move one
side of the body. Spasticity affects roughly 40% of stroke survivors and is characterized by
stiff or tight muscles that constrain movement (National Stroke Association®, 2012). The
primary treatment for these cases is rehabilitation, i.e., the process of helping an individual
achieve the highest level of independence and quality of life possible, physically,
emotionally, socially and spiritually. Where rehabilitation is possible, it involves many hours
of highly skilled procedures. The number of people capable of providing such support is
insufficient for adequately covering all patients that need help. Recovery progression varies
greatly and while certain people recover relatively quickly, for others, recovery can take a
very long time, and can even be a lifelong process.
The use of robotic assistance in rehabilitation is an important point of interest that is
attracting significant attention (Feriančik and Líška, 2014; Kurnicki, Stanczyk and Kania,
2014). Many studies have shown that robotic rehabilitation can be effective at improving arm
function following a stroke (Hesse, Schmidt and Werner, 2006; Kwakkel, Kollen and Krebs,
2008; Masiero, Armani and Rosati, 2011; Norouzi-Gheidari, Archambault and Fung, 2012;
Riener, Nef and Colombo, 2005). However, in studies where participants received an
equivalent amount of either robotic or conventional therapy, the improvements in arm
function were no longer significant (Norouzi-Gheidari, Archambault and Fung, 2012). One
reason for this may be that earlier studies used robotic devices with a limited number of
degrees of freedom, such as planar manipulandums. Indeed, a recent study (Klamroth-
51
Marganska et al., 2014) demonstrated a small but significant improvement in arm function
following therapy involving a 7-degree-of-freedom robot (shoulder, elbow and hand
opening) when compared to an equivalent amount of conventional therapy. Thus, there is a
clinical need for continuing the development of robotic devices that can assist with
naturalistic arm movements.
The ETS - Motion Assistive Robotic-exoskeleton for Superior Extremity (ETS-MARSE) was
developed in our laboratory (Ochoa Luna et al., 2014a; Rahman et al., 2011b; Rahman et al.,
2012b; Rahman et al., 2012c) in order to provide rehabilitation assistance for the upper
limbs. Currently, it comprises a seven-degree-of-freedom (DOF) exoskeleton, designed to
cope with the full motion capabilities of the human arm; that is, at the shoulder, elbow and
wrist levels, combined or individually. Additionally, it contains a graphical user interface that
uses a virtual environment with different rehabilitation exercises. To date, work in this regard
has been developed to the point of passive rehabilitation, which means that the exoskeleton
executes movements along predefined trajectories, while moving the subject’s arm with it to
help improve the range of movement. This paper describes the next rehabilitation step:
active-assistive and active rehabilitation (Brokaw et al., 2011; Dipietro et al., 2005; Krebs et
al., 2003).
The methodology presented in this paper combines the advantages of the trajectory tracking
control as the inner loop control of the robot and an admittance-based trajectory modifier that
performs the outer force control, and which is responsible for the interaction between the
robot and user. The admittance is used as a means of modifying the desired trajectory
(Culmer et al., 2010; Seraji, 1994). Due to the nonlinear nature of the ETS-MARSE, a
nonlinear control technique that has inherent adaptive characteristics has been used, i.e.,
virtual decomposition control (VDC). VDC is a relatively new approach that can reduce the
mathematical complexity of multi-degree of freedom robots and has an adaptive nature that
helps to deal with different patients’ dynamics (Zhu et al., 1997). As robots become more
complex, the computation of robot dynamics is proportional to the fourth power of the
number of DOF in Lagrangian dynamics (Zhu, Piedboeuf and Gonthier, 2006). VDC uses the
52
dynamics of virtually created subsystems to conduct control design; this decomposition
yields simpler dynamic equations in formulation and implementation (Zhu and De Schutter,
2002). In previous research with ETS-MARSE, we used different non-linear control
strategies, such as computed torque (CTC) (Rahman et al., 2011b) and sliding mode control
(SMC) (Rahman et al., 2012b). Though SMC performed well, it showed an approximately
1.5 times increase in end-effector tracking error when the conditions of the subject changed
and perturbations were presented, while the same exercise was performed. It also presented
the associated chattering, which can be reduced but not eliminated (Rahman et al., 2012b).
Conversely, an advantage of the VDC lies in its inherent adaptive capabilities, in the form of
internal parameter estimation. It was shown in our previous studies that in direct comparison
with CTC and PID, VDC can successfully cope with the physiological variations between
different subjects (Ochoa Luna et al., 2014b). Although differences in tracking error were
minimal and below the needs dictated by the application, PID showed an average RMS error
standard deviation more than three times larger than for VDC; for CTC, this was more than
10 times that of VDC. VDC however, due to control gains and parameter estimation gains,
involves a complicated process of initial tuning during the controller design process.
In order to obtain the user’s motion intention and modify the robot’s trajectory tracking
accordingly, the admittance concept is used. This approach has also been proven adequate for
high ratio transmissions systems (Calanca and Fiorini, 2014; Seraji, 1994). The robot takes
information from the human-machine interaction, in this case through contact force feedback
between the structure and the person’s arm and uses it to actively modify its rehabilitation
task.
In recent years, admittance control for rehabilitation has come to represent a well-known
approach and different schemes have been proposed (Colombo et al., 2005; Culmer et al.,
2010; Ozkul and Barkana, 2013; Younggeun et al., 2009). One of the main advantages of this
type of control is that it offers the possibility of active rehabilitation. This is because it
contributes to the rehabilitation process by allowing task repeatability and provides relevant
data for the quantification of different outcomes, such as improvement, effort, etc. However,
53
this approach is limited by the number of degrees of freedom of the robotic device (Ozkul
and Barkana, 2013) or has only been employed with end-effector type robots (Colombo et
al.; Culmer et al., 2010; Younggeun et al., 2009). The contribution of this paper is to present
both active-assistive and active rehabilitation task schemes for the 7DOF ETS-MARSE
exoskeleton. These tasks are based on path-tracking game-like exercises that have been
successfully employed in neuromuscular rehabilitation (Zhang, Davies and Xie, 2013). The
rehabilitation robot works in two different scenarios, both of which make use of a virtual
environment as an interface to visualize the movement to be performed. In the first scenario
(active-assistive rehabilitation), the robot follows a predefined movement path; however, the
system measures the user’s force opposing the predetermined movement and allows a certain
adjustable degree of trajectory variation. In the active mode, the robot allows the user to
freely move in the workspace while trying to achieve a target. In this case, the user’s
movement is constrained by means of virtual walls that restrain him from exceeding certain
limits and mark the point where the system will take corrective or assistive actions to help
resolve a collision conflict. At all times, the robot appears weightless to the user and helps to
support their arms if they stop in the middle of an exercise. These schemes may encourage
the patient to actively participate in the exercise by attempting to follow the target trajectory
and motivating them to improve their level of accomplishment.
This paper is organized as follows: section 3.2 describes the ETS-MARSE and the setup of
the system. In section 3.3, a general description of the controller (VDC) is given. In section
3.4, the implementations of the active-assistive and active rehabilitation schemes are
described. Section 3.5 summarizes the experimental setup and presents the results. Finally,
section 3.6 provides conclusions and future work perspectives.
3.2 System Overview
The exoskeleton robot arm ETS-MARSE is shown in Figure 3.1. It is an open chain, all-
revolute, 7DOF wearable manipulator-like robot; its joints were designed to correspond to
the principal degrees of freedom of the human arm. These are:
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3DOF at shoulder level for horizontal flexion/extension, vertical flexion/extension and
internal/external rotation;
1DOF for elbow flexion/extension;
1DOF for forearm pronation/supination;
2DOF at the wrist level for radial/ulnar deviation and flexion/extension.
Figure 3.1 Subject wearing ETS-MARSE robot arm
The exoskeleton structure has a six-axis force sensor mounted on the end-effector (tip) of the
robot, which is at the base of the handle where the user’s hand must be positioned. Each joint
is driven by a brushless DC motor that has a Hall effect sensor used for position feedback of
the joints. The motors are incorporated with harmonic drives; the specifications for the
motors and harmonic drives can be found in Appendix B. A backplane card collects analogue
and digital signals and connects through the proper interface cards to an NI PXI-7813R
(remote input-output card) placed on an NI PXI-1031 chassis. The card has an integrated
FPGA in which low-level control is performed, a PI controller for the current loop of the
motors, position feedback via the Hall effect sensors and the collection of force sensor inputs.
55
A PXI-8108 controller, which performs high-level control (the robot operating system and
the trajectory tracking controller) is also mounted on the chassis. In this case, we are using
the nonlinear control technique known as virtual decomposition control (VDC) (Zhu et al.,
1997), with an update rate of 1 ms. A description of the implementation of the VDC is
outlined in section 3.3 of this paper.
A PC runs the human-machine interface virtual environment in which the robot wearer
visualizes the rehabilitation exercise. The current architecture of the system is depicted in
Figure 3.2. Since the system is a human-machine interface, safety is a major concern and for
this reason, a hardware emergency stop button is built into it.
Figure 3.2 ETS-MARSE system hardware overview
3.3 Virtual Decomposition Control of the ETS-MARSE
The control technique we used is presented in this section, but only the steps required to
implement VDC are listed. This technique presents an effective approach for dealing with
high DOF robots and multi-robot control. A detailed analysis is beyond the scope of this
paper; readers interested in such an analysis are referred to other works that address this
technique (Zhu and De Schutter, 1999; Zhu et al., 2013). The frame attachment for the DOF
of the ETS-MARSE, following the method summarized in (Craig, 2005), is shown in
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Figure 3.3. The resulting Denavit-Hartenberg modified parameters are obtained, as described
in (Craig, 2005), and are summarized in Table 3.1.
Table 3.1 ETS-MARSE Denavit-Hartenberg modified parameters
i αi-1 ai-1 di θi
1 0° 0 d1 θ1
2 -90° 0 0 θ2
3 90° 0 d3 θ3
4 -90° 0 0 θ4
5 90° 0 d5 θ5
6 -90° 0 0 θ6-90º
7 -90° 0 0 θ7
Figure 3.3 7DOF exoskeleton robot arm
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3.3.1 Robot subsystem decomposition
The first step in the VDC analysis covers the virtual decomposition of the robot; in our case,
we can view the exoskeleton as a single open chain. This results in decomposition into
fourteen subsystems, as illustrated in Figure 3.4.
Figure 3.4 Virtual decomposition in 14 subsystems
3.3.2 Kinematics
From the resulting parameters shown in Table 3.1 and the decomposition shown in Figure
3.4, the homogeneous transformation matrices of the system are obtained. From these, the
force/moment transformation matrices of the robot are calculated as follows:
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= 0 ×( ×) ∈ ℝ × (3.1)
where represents the rotation matrix from one frame to the next and is the
distance between frames, and:
( ×) = 0 − (3) (2) (3) 0 − (1)− (2) (1) 0
(3.2)
where ( ) represents the term of the vector.
We calculate each force/moment transformation matrix for = 1,… ,6.
The next step is to calculate , the linear/angular velocity vectors of the frames (with = 1,… ,7) as follows:
= ∈ ℝ (3.3)
where is the linear velocity vector and is the angular velocity vector of the
corresponding frame. With the previous linear/angular velocity vectors, the augmented
velocity vector is formed as:
= [ ⋯ ⋯ ] (3.4)
Equation (3.4) can be written in the following form:
= ∗ (3.5)
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where = [ ⋯ ] is the velocity vector and is the VDC-Jacobian matrix of the
system:
= 0 ⋯ 0 ⋱ ⋮⋮ ⋱ ⋱ 0…
(3.6)
with = [0 0 0 0 0 1] , is a 7 × 7 identity matrix and 0 a 6 × 1 zero vector.
Finally, the required velocities need to be calculated as a function of the control
requirements. Since in our case the robot is required to track a control trajectory, we
incorporate the desired position in the vector of required velocities:
= + ( − ) (3.7)
where = [ ⋯ ] is the required velocity vector, = [ ⋯ ] is the
desired velocity vector, > 0 is a control parameter, = [ ⋯ ] is the desired
position vector and = [ ⋯ ] is the position vector. From (3.5) to (3.7), we obtain
the augmented required velocity vector as follows:
= ∗ (3.8)
3.3.3 Dynamics
In this paper, only the inverse dynamics that take part in the control of the robot are
described. To obtain the inverse dynamics, it is necessary to calculate the forces required for
the links and then the torques required by the joints. The first step for the link dynamics is to
obtain the required net force/moment vectors using the following equation:
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∗ = + ( − ) (3.9)
for = 1,… ,7, where is a symmetric positive-definite gain matrix; the velocities and are defined in relations (3.3) and (3.8), respectively; ∈ ℝ × is a regressor matrix
and ∈ ℝ is the estimated parameters vector composed of the mass of the link, the
elements of the vector pointing from the origin of the reference frame of the link toward its
mass centre, as well as the elements of the inertia tensor of the body. The exact
representation of each element of is given in Appendix A. To estimate the parameters, the
following relation is used:
= ( ), , ( ), ( ), (3.10)
for = 1,… ,7 and = 1,… ,13. Where represents the th parameter of the th link, is
the parameter update gain, ( ) and ( ) are the lower and upper bounds of
respectively and ( ) ∈ ℝ is a scalar variable given by:
= ( − ) (3.11)
The projection function is a differentiable scalar function defined for ≥ 0, such that its
time derivative is governed by:
= ( ) (3.12)
with:
= 001 ≤ ( ) ( ) ≤ 0 ≥ ( ) ( ) ≥ 0ℎ
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Once this step is completed, the required force/moment vectors at the cutting points are
obtained as follows:
= ∗ = ∗ +
(3.13)
for = 6,… ,1. The next step is the calculation of the dynamics of the joints. Some relations
and variables used to calculate the dynamics of the joints were also used in the calculation of
the dynamics of the links; therefore, a sub-index, , is used to refer to the joints’ dynamic
equations and variables. For = 1,… ,7 in (3.14) to (3.18), the following vectors are defined:
= [ ( ) 1] (3.14)
= [ ] (3.15)
where is the equivalent mass or moment of inertia, > 0 denotes the Coulomb friction
coefficient, > 0 denotes the viscous friction coefficient and denotes an offset that
accommodates asymmetric Coulomb frictions. As in the case of the links, the estimation of
the parameters defined in (3.15) is performed as follows:
= ( ), , ( ), ( ), (3.16)
However, in this case, = 1,… ,4 and the scalar function is defined for the joints as:
= ( − ) (3.17)
Thereafter, the net torque for the joint becomes as follows:
∗ = + ( − ) (3.18)
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where denotes a feedback gain.
Finally, the torques obtained from the link and joint analyses are combined. First, we extract
the torque of the link force/moment vector.
= (3.19)
for = 1,… ,7. With z defined after (3.6), the control torque is then designed for = 1,… ,7
as:
= ∗ + (3.20)
For a complete stability analysis of VDC, the reader is referred to (Zhu et al., 2013; Zhu et
al., 1997; Zhu, Zeungnam and De Schutter, 1998). Figure 3.5 presents a flow diagram of the
VDC architecture applied in the inner position control loop. The interaction between the
robot and the human is represented by the human joint position , causing the robot to exert
torque . The human also applies force, ℱ, which will be used in the outer force control
loop, as described in the next section.
Figure 3.5 Block diagram of the VDC
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3.4 Active-assistive and active rehabilitation
In robotics, a trajectory defines movement of a robot in a multidimensional space. This
trajectory contains information concerning the position, velocity and acceleration for each
degree of freedom in time (Craig, 2005). To control the movement of the robot, the user
defines a desired trajectory that includes this information and is usually generated by means
of a trajectory planner.
3.4.1 Trajectory planner
The trajectory planner for ETS-MARSE is based on joint-space specification. It is performed
in real time on a dedicated processor (PXI-8108), described in section 3.2. Some exercises
can comprise different trajectory segments, each specified by initial and final positions for
each joint. Each segment of the trajectory for each joint is calculated using a cubic
polynomial (Craig, 2005) of the form:
( ) = + + + (3.21)
where for = 0,… ,3 are the coefficients of the cubic polynomial to be specified. With
initial and final velocities of zero, the initial position defined as (0) = and the final
position defined as = , equation (3.21) reduces as follows:
( ) = + 3( − ) − 2( − )
(3.22)
In order to obtain information on the velocity and acceleration of the trajectory, the
corresponding first and second derivatives of (3.22) are used.
In rehabilitation, it is often useful to specify a desired trajectory in Cartesian space in order to
specify movements with a physical interpretation. This can be as simple as a straight line, or,
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for example, following a geometrical shape such as a triangle, a rectangle, etc. In the case of
the ETS-MARSE robot, the trajectory can be specified either in the joint space or in
Cartesian space (robot workspace); whatever the case, the trajectory tracking is always
executed in joint space. Thus, it is necessary, given a position and orientation of the end-
effector in Cartesian space, to find the joint positions of the robot that can accomplish this
desired configuration (inverse kinematics problem). In this case, the pseudo-inverse of the
Jacobian method is used.
In the dynamic relations of the links of a robot, the reference frame of each link has linear
and angular velocities, with respect to the other links and to the robot reference frame. The
Jacobian matrix of a robot relates the joint velocities with linear and angular velocities of the
Cartesian space as follows:
= ( ) (3.23)
where ∈ ℝ is the velocity vector of the end-effector, ∈ ℝ is the joint velocities vector
and ( ) ∈ ℝ × is the robot Jacobian matrix. For the inverse kinematics problem
presented, one possible solution can be obtained as follows (Asada and Slotine, 1986):
= ( ) (3.24)
where ( ) = ( ) ( ( ) ( ) ) is the generalized pseudo-inverse. The method can be
enriched by adding null space characteristics to the right side of the equation with the
term( ( ) ( ) − ) , where ∈ ℝ is an arbitrary vector that can be used for tasks such as
obstacle avoidance and is the 6 × 6 identity matrix. Being a redundant robot, the ETS-
MARSE has different solutions for its inverse kinematics problem; currently, to solve that
problem, we are developing an inverse kinematics solution (analytical, geometrical or
numerical) that will ensure anthropomorphic configurations, as in (Culmer et al., 2010;
Zhang, Xiong and Wu, 2011). In the rehabilitation tasks presented here, solving the null
space is not necessary, since only predefined Cartesian trajectories were used. These
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trajectories were simulated and tested to constantly ensure a configuration of the robot not
presenting any non-ergonomic positions. Additionally, singularity avoidance is secured with
joint angle limits, both in software and hardware (mechanical stoppers).
3.4.2 Active-assistive rehabilitation based on an admittance-modified trajectory
planner
In the case of active-assistive mode, the robot helps the user, at an adjustable level, to
achieve the tracking of a trajectory shown in the virtual interface. To do this, the assistive
controller somewhat modifies the predefined trajectory in relation to the patient’s movement
limitations. The system measures the force exerted by the user at the end-effector of the
robot, which can be interpreted as the difference between the user’s trajectory and the goal
trajectory.
The first step is to transform this information into a quantity that specifies how the subject’s
opposition force affects all the DOF of the exoskeleton (that are related to the human arm
joints). As a consequence of the virtual work principle, the Jacobian matrix relates static
forces, i.e., it transpose assigns Cartesian forces to joint torques as follows:
= ℱ (3.25)
where is the 7 × 1 vector of joint torque and ℱ is the 6 × 1 measured force-moment
Cartesian vector. This relation gives us the user’s opposition force in terms of joint torques.
The second step is to transform these torques into meaningful information for the trajectory
that is being followed, that is, information relating to changes in position. Impedance can be
defined as a transfer function between the external force acting on the manipulator and its
displacement (Gorinevsky, Formalsky and Schneider, 1997). Knowing the result from (3.25)
and applying the impedance definition in the form of an admittance relation, which directly
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relates an input force to an output position, we have a direct form with which to modify the
desired trajectory as follows:
= + 1+ (3.26)
where is the 7 × 1 vector of the new desired trajectory defined by the admittance, is
the 7 × 1 vector with the original desired trajectory from the trajectory planner and the final
right term of the equation in the parenthesis, the chosen admittance function. It can be seen
that the latter has the form of a spring-damper function, in which is the 7 × 1 vector of
torques exerted on the robot’s joints by the subject, calculated from (3.25) and and are
the 7 × 7gain matrices corresponding to the spring and damper constants, respectively. By
adjusting these constants to provide higher or lower opposition to the subjects’ disturbances
and constraints over movement, this admittance function allows for variation in the amount
of help to be provided by the robot. This particular admittance function by means of the
damping term also provides smooth movement.
3.4.3 Active rehabilitation based on an admittance-modified trajectory planner
Another application of an admittance function modifying a predefined trajectory involves
performing a free trajectory movement. If the spring-damper system introduced by the
admittance function in (3.26) is detached from a desired trajectory, it becomes a means of
moving the robot freely within its workspace. In this case, the subject is allowed to move in
the environment presented by the virtual interface and can try to follow the trajectory without
any robotic aid. This rehabilitation option, corresponding to active (unassisted) rehabilitation,
is achieved by changing the desired trajectory of the robot, that is, in (3.26). Instead of
coming from a trajectory planner, the desired trajectory comes from the robot’s previous
position, as follows:
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= + 1+ (3.27)
where is the 7 × 1 vector of the joint positions. If the user stops exerting forces on the force
sensor, → 0, causing the robot to reduce its movement and gradually, when = , the
robot remains in its most recent position. With this mode, the robot is allowed to follow the
user‘s movements, while the trajectory tracking ensures the weightless sensation of the robot
structure to the subject and provides gravity compensation. In Figure 3.6, a block diagram
showing the control architecture is presented. The position of the selector shown in the
bottom row of the system corresponds to the case of active-assistive rehabilitation (left
position) and active rehabilitation (right position) described earlier. In this case, the desired
trajectory that inputs the VDC (see Figure 3.5) is the admittance modified trajectory from
(3.26) or (3.27) and ∆ is the second term of the right-hand side of the same relations.
Figure 3.6 Block diagram of the system
The ETS-MARSE works in two different active rehabilitation modes, which use virtual walls
added to the environment in order to constrain movement to a confined space. In the first
mode, the system restrains movement beyond the wall and only allows movement that
corrects the collision situation, i.e., the robot will not allow the user “to slide” through the
wall to complete the exercise. The user must return to the inner part of the space in order to
continue with the movement. The algorithm used in this rehabilitation mode is presented in
Figure 3.7. The second mode of operation is intended for users that need more assistance
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once there is a deviation from the main trajectory. Once the user hits a wall, the robot stops
for a predetermined time to let the user notice that movement has been stopped by the
system. It then goes into passive mode, which means that the robot will help the user by
returning automatically to the closest point on the desired trajectory, as illustrated in Figure
3.8. Here, Pw represents the point where the user hits the wall, Pi the trajectory initial point,
Pf the final point and Pr the point of the position reset. The last one, the closest point to the
trajectory, is obtained as follows: first, the cosine of angle is calculated:
= | ⋅ + ⋅ + ⋅ |+ + ⋅ + + (3.28)
where ∈ ℝ and ∈ ℝ are the direction vectors of the lines ( ) and ( ), respectively, and and are the elements of the corresponding direction vector. Then,
the reset point is calculated as:
= ⋅ + + + (3.29)
Figure 3.7 Active rehabilitation with walls
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Figure 3.8 Virtual wall collision and reset path
With the final point obtained from (3.29) and the initial point as Pw, the passive mode of the
system conducts the robot end-effector to this point by means of a trajectory generated as
described in subsection 3.4.1. Finally, after another predetermined time to allow the user to
be ready, the system allows them to continue. The algorithm followed by this rehabilitation
mode is presented in Figure 3.9.
Figure 3.9 Active-assisted rehabilitation with walls
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3.5 Experimental results
In this section, we present one scenario for each of the two rehabilitation modes. The first
comprises an experiment performed for active-assistive rehabilitation and the second, two
tests for active rehabilitation.
3.5.1 Active-assistive rehabilitation
This first scenario comprises three tests based on a tridimensional square trajectory, defined
below. The trajectory involves the movement of the seven degrees of freedom of the robot.
Test number one is given as a reference of the behaviour of the robot, i.e., without modifying
the trajectory tracking. This scenario corresponds to the passive rehabilitation mode in which
the patient is guided through a predefined rehabilitation exercise. The result of this test is
shown in Figure 3.10. It can be seen that the tracking error is very small and this will be used
as a reference value. The initial position of the end-effector of the robot corresponds to point
A; it moves to points B – C – D and then returns to A. The points are listed in Table 3.2.
Figure 3.10 Reference trajectory tracking
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Table 3.2 Robot active-assistive rehabilitation reference trajectory
Point X(cm) Y(cm) Z(cm)
A 28.67 2.51 37.08
B 28.67 -12.51 37.08
C 43.67 -12.51 27.08
D 43.67 2.51 27.08
The next two tests constitute the central point of this approach of rehabilitation (active-
assistive). In these cases, the tracking is modified based on the measurements of the force
sensor. The reference trajectory is the same as that presented in Figure 3.10, but modified
according to equation (3.26). To simulate stiffness or spasticity from the user, an elastic band
is tied from the handle of the robot (which holds the force sensor) to an external anchor point.
This provides a systematic comparison, depending only on the modification of the
admittance parameters. The setup allows the variation to be independent from the test
subject, whose behaviour can change from one test to another. For the first test, the
admittance parameters were selected to provide a high degree of help, specifically with the
main diagonal of = [0.050.060.060.050.020.020.02] and the remaining elements
equal to 0, and the main diagonal of = [51510555] . The remaining elements were
also zero. The second test was configured to provide a low degree of help from the robot, i.e.,
with the main diagonal of = [0.10.120.120.10.040.040.04] and the main diagonal of = [51510555] , and the remaining elements being zero.
The results of these tests are shown in Figures 3.11 and 3.12 for high and low degrees of
help, respectively. Because the opposition force to this movement is exerted on the robot, the
actual trajectory is deflected from the predefined one. In these figures, the dotted line
represents the desired trajectory and the solid line the actual trajectory followed by the robot,
which was perturbed using the elastic band.
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Figure 3.11 Trajectory modified with high degree of help
Figure 3.12 Trajectory modified with low degree of help
For the final two tests (Figures 3.11 and 3.12), the force and torque measured with the force
sensor are shown in Figure 3.13. We can see how the force input from the elastic band is very
similar in both tests; nevertheless, the modification of the trajectory is different, allowing us
to see the effects of modifying the admittance function coefficients.
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Figure 3.13 Comparison of forces-torques between high and low degree of assistance from the robot
3.5.2 Active rehabilitation, constrained free movement
In this rehabilitation mode, the user follows the trajectory by means of a virtual interface that
provides the tracking of movement and incorporates a variety of exercises in a game-based
environment. The active rehabilitation mode with virtual walls has two different tests: the
first with the wall as an obstacle and the second, where collision with the wall indicates that
the robot will assist the user, as described in section 3.4. Both setups require the subject (32-
year old healthy male subject with a mass of 91 kg and height of 182 cm, in seated position)
to track a straight line; the virtual wall is located parallel to the desired trajectory, 10 cm to
the right.
The result for the first experiment is shown in Figure 3.14. In this mode, once the user hits
the wall, the system only allows movement towards the desired trajectory. In the plots at the
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bottom of the figure, the filtered force in the Y-axis of the force sensor and the position of the
end-effector in the Y-axis of the reference frame are shown as a function of time. Both axes
are the Y-axis, because the wall is set in the Y-direction. The Y-axis of the force sensor is
parallel to the Y-axis of the reference frame, but in the opposite direction, which provides a
good reference point for the comparison. Nevertheless, it is very important to remember that
the force and its modification follow the transformation described in (3.25) and (3.27). It can
be seen that, when the subject starts to apply force to the sensor at 12.86 seconds, the
displacement of the robot starts. At 17.05 seconds, the wall is hit; the virtual wall restricts the
movement of the end-effector beyond this point (at approximately 0.08 m), irrespective of an
increase in the user’s produced force. Finally, at 20.40 seconds, when the user starts to apply
force in the opposite direction (away from the wall), the system allows the robot to continue
with the movement and completes the exercise.
Figure 3.14 Virtual walls as obstacle for active rehabilitation
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The final test shows the assisted wall return. It can be seen in Figure 3.15 that the user starts
the movement by applying force to the robot at 8.31 seconds. Once the wall is hit, at
approximately 10.90 seconds, it can be seen that the movement of the robot stops, even
though force continues to be exerted for some time. The system, after an idle waiting time
(three seconds), resets the position to the closest point in the trajectory (two seconds),
followed by another idle time (three seconds), allowing the user to be ready. After this, the
user can continue the exercise when ready, in this case, at 20.06 seconds. It is important to
note that in the two idle states and in the reset state, there is no input from the user to the
force sensor. This shows that assistance is provided for the system without any action needed
from the user. The small delays that can be observed in the state changes, especially from the
applied force to the start of movement, are due to the time it takes to overcome the static
friction and the filtering in the force sensor’s raw data; this delay is imperceptible to the user.
Figure 3.15 Virtual walls as obstacle and starting point for robotic assistance in active rehabilitation
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3.6 Conclusions
The experimental results confirm that the present work can actively help in different
rehabilitation scenarios. For active-assistive rehabilitation, with the guidance of the ETS-
MARSE, a subject can accomplish a specified trajectory. The robot can vary the assistance
provided according to the evolution and the needs of future patients. It is important to note
that the robot will not produce forces that are beyond the capabilities of the subject in order
to fulfil a trajectory. A qualified therapist must adjust the limits according to the user’s
requirements. The amount of variation of the trajectory can be quantified as an excellent
measurement of progression of the subject. In the case of active rehabilitation, it is shown
how by means of the same admittance function, the system can work in a free movement
mode. This rehabilitation mode, combined with limits (virtual walls), could indicate when
patients will need assistance from the robot to complete their rehabilitation tasks. As the next
step for active rehabilitation, the system will incorporate the use of electromyographic
signals in order to complete the readings of the force sensor and to provide better tracking of
the subject’s movement intentions, and will be used on its own for subjects where the force
sensor may be not enough to determine the intended movement.
CHAPTER 4
COMPLIANT CONTROL OF A REHABILITATION EXOSKELETON ROBOT ARM WITH FORCE OBSERVER
Cristóbal Ochoa-Luna1, Maarouf Saad1, Jawhar Ghommam2, Mohammad Habibur Rahman3
and Philippe S. Archambault4,5 1Department of Electrical Engineering, École de technologie supérieure,
1100 Notre-Dame West, Montreal, Quebec (H3C 1K3) Canada. 2National Institute of Applied Sciences and Technology, University of Carthage,
Centre Urbain Nord BP 676-1080, Tunis Cedex, Tunis, Tunisia. 3Mechanical Engineering Department, University of Wisconsin-Milwaukee,
3200 North Cramer Street, Milwaukee, WI (53211) USA. 4School of Physical & Occupational Therapy, McGill University, Canada.
3654 Prom Sir-William-Osler, Montréal, Québec (H3G 1Y5) Canada. 5Centre for Interdisciplinary Research in Rehabilitation (CRIR), Canada.
2275 Laurier Avenue East, Montréal, Quebec (H2H 2N8) Canada.
This paper was sent to the IEEE/ASME Transactions on Mechatronics in March 2016
Abstract:
In robotic rehabilitation, active rehabilitation is a phase in which interaction between human
and robot allows the subjects to perform daily exercises. One key element of this interaction
is the force applied by the subject. This force can be measured by a force sensor or estimated
using a nonlinear force observer. In the approach presented in this paper, the nonlinear
observer estimates the interaction forces between the subject and the robot, in order to
understand the intention of motion of the subject. Then, by means of an admittance function,
this estimation is used for compliance control, so that the robot moves while following the
user’s intention. This method allows the subject to perform some active isokinetic-type
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rehabilitation exercises. Experimental results show the effectiveness of the proposed
approach.
Keywords: Active Rehabilitation, Compliance Control, Exoskeleton Robot, Nonlinear
Observer, Virtual Decomposition Control
4.1 Introduction
According to the World Health Organization, 15 million people worldwide suffer a stroke
each year; of these, 5 million die and another 5 million are left with long-term disabilities
(Mackay and Mensah, 2004). Stroke has been identified as one of the major causes of loss of
upper extremity (UE) function. One of the most common effects after a stroke is weakness or
paralysis on one side of the body (hemiparesis), which affects up to 90 percent of stroke
survivors (Van der Loos and Reinkensmeyer, 2008). When rehabilitation is possible, it
implies many hours of highly skilled and extensive therapy. In the last years, the demand for
rehabilitation services has increased significantly. As a result, the number of clinicians
available to provide therapy is not sufficient to deal with the number of patients (Bureau of
Labor Statistics, 2015; Gupta, Castillo-Laborde and Landry, 2011; Landry, Ricketts and
Verrier, 2007). Therefore, robotic-assisted UE rehabilitation has become very important and
has shown some promising results (Huang, Tu and He, 2015; Klamroth-Marganska et al.,
2014; Norouzi-Gheidari, Archambault and Fung, 2012; Patton et al., 2006). It is for that
reason that we have developed the ETS - Motion Assistive Robotic-exoskeleton for Superior
Extremity (ETS-MARSE). The project has been developed in different stages (Rahman et al.,
2011a; Rahman et al., 2012a). The latest version comprises of a seven degree-of-freedom
(DOF) exoskeleton, designed to cope with the main motion capabilities of the human UE;
that is at the shoulder, elbow and wrist levels, in combination or individually. It also contains
a graphic interface to a virtual environment with different rehabilitation exercises (Ferrer et
al., 2013). In active rehabilitation, the subject performs a rehabilitation task and the robot
interacts with the subject to control (e.g. time limits, space limits, etc.) or, as in the case of
this paper, to present variable resistance to the movement (i.e. isokinetic exercise). This
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behavior emphasizes the responsibility of the patient in being active to accomplish the
exercise.
The interaction between the patient and the robot can be implemented through different
methods: from buttons and joysticks in the first rehabilitation robots to electromyography
(Kiguchi and Hayashi, 2012) and electroencephalography (Frisoli et al., 2012; He et al.,
2015) in recent ones. The use of force transducers is one of the most widely used approaches
(Jackson et al., 2007; Miller and Rosen, 2010; Ochoa Luna et al., 2015; Ozkul and Barkana,
2013; Zhou and Ben-Tzvi, 2015). Upper extremity rehabilitation by means of the robot-
human interaction forces principally makes use of compliant control as admittance and
impedance (Gupta and O'Malley, 2006; Otten et al., 2015). These systems use transducers to
measure the force and torque exchanges between the exoskeleton and the user or the
exoskeleton and the environment. For example, the iPAM dual robot system uses two
manipulator-like robots, with a total of 6DOF, to hold the patient’s arm at that level of the
upper arm and forearm, with two 6DOF force transducers (Jackson et al., 2007). The
RehabRoby, a 6DOF exoskeleton, uses two one-axis force sensors mounted dorsally in the
forearm strip; one to measure the force applied to the elbow flexion movement and the other
for the shoulder flexion movement (Ozkul and Barkana, 2013). The EXO-UL7, a 7DOF
wearable upper limb exoskeleton, uses four 6-axis force/torque sensors; one at each
attachment point (upper arm, lower arm and hand) and one at the tip of the exoskeleton
(Miller and Rosen, 2010). In our previous studies with the ETS-MARSE, we have
demonstrated the feasibility of rehabilitation work with the aid of compliance control for
robotic rehabilitation with the use of a 6DOF force sensor mounted at robot’s endpoint
(Ochoa Luna et al., 2015). All the above-mentioned systems have shown they can provide
users with satisfactory rehabilitation exercises. However, some problems with the use of
force sensors may arise, such as cost, sensibility to temperature changes, noise and unstable
states caused by the narrow bandwidth of force information (Katsura, Matsumoto and
Ohnishi, 2007), etc. There is also the fact that small sensors, although very precise, are
susceptible to be damaged during human-robot interaction.
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In this paper we present the use of a nonlinear observer, that have been previously
investigated for industrial applications (Alcocer et al., 2003; Chan, Naghdy and Stirling,
2013; Do and Pan, 2008; Wen-Hua et al., 2000), applied to a rehabilitation robot (ETS-
MARSE) to avoid the need for a force sensor. Applications of disturbance observers for
rehabilitation have been presented before (Gupta and O’Malley, 2011; Popescu et al., 2013).
In the first paper, a nonlinear disturbance observer was applied successfully to control
external forces to a 1DOF rehabilitation mechanism. In the second one, a trio of nonlinear
observers (force observer, velocity observer, and force-disturbance observer) was used to
control a hand exoskeleton system for rehabilitation. The performance of the system was
demonstrated by numerical simulation. In the work presented in this paper, the force
estimated by the proposed force observer was used to detect the subject’s movement
intention and to apply a compliance force control to move the robot-human system. This
approach also simplifies the use of an admittance function to modify the current position of
the robot and perform a compliant movement. Indeed, with a force observer, the torque
applied to each joint can be estimated directly; i.e. it is no longer necessary to transform the
force measured in Cartesian space by a force sensor to joint space using a Jacobian inverse.
The impedance of the robot-human system due the admittance function is used to
characterize the isokinetic-type exercises. Another key aspect is the study of the effects of the
control based on the nonlinear observer in a multi-degree-of-freedom robot (7DOF). Finally,
in order to better separate the effects of the friction from the human interaction forces (as
these could be seen as disturbance), the friction estimated by the controller (see section 4.2)
is fed back into the observer, in order to precisely discard the effects of the position
controller friction-compensation part.
This paper is organized as follows. Section 4.2 presents the nonlinear position control. In
section 4.3, the compliance control that includes the nonlinear force observer is described.
Section 4.4 describes the hardware architecture and experimental setup of the system and its
results. Finally, section 4.5 provides the conclusions and future work.
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4.2 Nonlinear control: Virtual Decomposition Control and Force Observer
In this paper, the Virtual Decomposition Control (VDC) technique is used for the nonlinear
control of the robot. In previous studies with the ETS-MARSE (Ochoa Luna et al., 2014b),
VDC has proven that besides the performance in position control, it can successfully address
two important issues: a) it facilitates the implementation in a high degree-of-freedom robot
(7DOF in this case) through its subsystem decomposition, and b) it copes with the changes in
the dynamics of the robot-human system due to the biomechanical and physiological
characteristics of different patients through its internal dynamic-parameters adaptation.
Therefore, this technique was adopted as the current control method for our robot.
Additionally, as mentioned, the estimated friction parameters are used to feedback the
controller friction compensation to the nonlinear observer.
This section shows only the kinematics analysis of the ETS-MARSE robot in order to present
it to the reader. A detailed analysis of the VDC implemented in the ETS-MARSE is
described in (Ochoa Luna et al., 2014b) and for a complete analysis of VDC, interested
readers can refer to (Zhu and De Schutter, 1999; Zhu et al., 2013). The frame attachment for
the ETS-MARSE is shown in Figure 4.1. The corresponding Denavit-Hartenberg modified
parameters are summarized in Table 4.1.
4.2.1 Nonlinear force observer
The development of the force observer was realized following the concept presented in
(Hacksel and Salcudean, 1994; Nicosia and Tomei, 1990). We can define the dynamics of a
robot manipulator as:
( ) + ( , ) + + ( ) = + ( ) (4.1)
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Figure 4.1 7DOF exoskeleton robot arm
Table 4.1 ETS-MARSE Denavit-Hartenberg modified parameters
i αi-1 ai-1 di θi
1 0° 0 d1 θ1
2 -90° 0 0 θ2
3 90° 0 d3 θ3
4 -90° 0 0 θ4
5 90° 0 d5 θ5
6 -90° 0 0 θ6-90º
7 -90° 0 0 θ7
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where is the force exerted at the end effector of the robot from the subject, ( ) is the
transpose of the Jacobian matrix of the system and the vector of control torques. ( ) is
the inertia matrix of the system, ( , ) the Coriolis and centrifugal matrix in Cristoffel
form, ( ) the gravity vector and represents the viscous friction coefficients. We define
the state variables as:
= =
(4.2)
replacing (4.2) into (4.1) and solving for the joint acceleration we obtain:
= ( )[− ( , ) − − ( ) + + ( ) ] (4.3)
The state variables can be estimated as follows, considering the system without external
perturbations (user exerted force):
= + (4.4)
= ( ) − , − − ( ) + + (4.5)
where and are two 7 × 7 symmetric positive definite gain matrices. The estimation
error is defined as:
= − (4.6)
given from (4.2) that = , subtracting (4.4) from yields:
= − (4.7)
then subtracting (4.5) from (4.3) and given that in Lagrangian robotic systems, for two
vectors ∈ ℝ and ∈ ℝ , ( , ) = ( , ) (Nicosia and Tomei, 1990) yields:
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= − = ( ) − ( , ) + , − − + ( )− = ( ) − ( , ) + , − + ( ) − = ( ) − ( , ) − , − + ( ) −
(4.8)
differentiating (4.7) with respect to time, gives:
= − = ( ) − ( , ) − , − + ( ) −−
(4.9)
therefore, we can obtain the force that the user applies to the robot:
( ) = ( ) + ( , ) + , + + ( ) + (4.10)
In order to simplify the computational complexity of (4.10), it has been demonstrated that a
good estimation of the external force can be obtained using only the last right-side term of
it (Alcocer et al., 2003). For a slow time varying environmental force, we can obtain and
estimated as follows:
= ( ) (4.11)
where ( ) is the generalized Jacobian pseudo-inverse and is the estimated force due to
the human.
Remark: In our case, it is not necessary to determine the Cartesian external force, since the
estimated joint torques are used directly as it will be explained in the admittance section.
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Finally, the torque due to friction is often hard to model accurately. VDC provides a way to
estimate the friction torque in each joint by its internal parameter estimation. To use a more
precise real-time friction model, we use these parameters and the model proposed by the
controller and the friction term in (4.5) can be replaced as follows:
= sign + + (4.12)
where is the vector of estimated Coulomb friction coefficients, is the vector of
estimated viscous friction coefficients and the vector of asymmetric Coulomb friction
offsets.
4.2.2 Stability Analysis
Theorem 1: Suppose the control input is such that the solutions for the robot dynamics
(4.1) exist, and consider the observer (4.4) and (4.5) where the observer gains and are
chosen such that are diagonal positive matrices and = − , where > , results
in the convergence of the estimation error states → 0 and → 0 as → ∞.
Proof: To obtain the error dynamics, take the time differentiation of (4.4) as follows:
= + (4.13)
then substituting (4.5) into (4.13) we obtain:
= ( ) − , − − ( ) + + + (4.14)
subtracting (4.14) from (4.3) we get:
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( ) + ( , ) − ,= ( ) − ( ) − −
(4.15)
and finally we obtain:
( ) = ( ) − ( ) − , − ( , ) −−
(4.16)
Consider the following Lyapunov function candidate:
= 12 ( ) (4.17)
the time derivative of (4.17) along the solutions of (4.16) is:
= ( ) + 12 ( ) (4.18)
substituting (4.16) into (4.18) and grouping terms we have:
= − − ( ) + + ( ) + , +− ( , ) + 12 ( )
(4.19)
then, given that the matrix ( ) − 2 ( , ) is skew-symmetric:
= − − ( ) + + ( ) + , + (4.20)
Taking from (4.11) that ( ) = , we obtain:
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= − ( ) + , + (4.21)
finally, it can be established that:
= − ( ) ≤ − (4.22)
where β is a positive constant and = − > 0. Since ( ) is uniformly positive
definite, the Lyapunov function in (4.17) is positive definite in . Since ≤ 0,V is also
bounded, and therefore is bounded and therefore is also bounded. To apply Barbalat’s
lemma, let us check the uniform continuity of . Differentiating (4.22) yields:
≤ −2 ( − ) (4.23)
This shows that is bounded since and are bounded. Hence is uniformly continuous.
Using Barbalat’s lemma, we have → 0. From (4.7) it can be concluded that → 0, from
(4.8) it can be concluded that → 0 as → ∞ and therefore by construction from (4.7) it
can be inferred that → 0 as → ∞.
4.2.3 Admittance control
In order to control the movement of the robot from the user’s force, a compliance control
based on admittance is used. An admittance function can be defined as a transfer function
that has a force as an input signal and yields a motion as the output signal and can be
expressed as follows:
= + (4.24)
where is the 7 × 1 vector of the new desired trajectory defined by the admittance, is
the 7 × 1 vector with the current position and the last right term of the equation, the chosen
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admittance function. This is the form of a spring function in which is a 7 × 7gain matrix
that corresponds to the spring constant and is the 7 × 1 vector of estimated torques exerted
towards the robot joints by the subject as consequence of his intention of movement. To
calculate this torque, we use the virtual work principle to substitute the left-hand side of
(4.10); hence (4.11) becomes:
= (4.25)
Because of this substitution, the Cartesian external forces don’t need to be calculated and
problems with the inverse of the Jacobian needed in (4.11) are eliminated. If the user stops
exerting forces, → 0 making the robot reduce its movement and gradually, when =the robot remains in its last position. With this, the robot is allowed to follow the user’s
intention of movement while the trajectory tracking ensures the gravity compensation.
4.3 Experimental results
In this section a brief description of the system architecture is given; afterward the
experimental setup is presented. The experiment consists of two scenarios. The first one is
based on an active joint-space task in which the subjects were asked to perform an elbow
flexion-extension and shoulder external-internal rotation. The second scenario is based on
active Cartesian-space task; in this case, the subject was asked to follow a straight line
presented in the virtual interface.
4.3.1 System architecture
The ETS-MARSE is shown in Figure 4.2. It is a manipulator like, open chain, 7DOF (all
revolute) wearable robot. It was designed for its joints to correspond to the principal degrees
of freedom of the human arm:
3DOF at shoulder level for horizontal flexion/extension, vertical flexion/extension and
internal/external rotation,
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1DOF for elbow flexion/extension,
1DOF for forearm pronation/supination, and
2DOF at the wrist level for radial/ulnar deviation and flexion/extension.
The exoskeleton structure has a handle mounted in the end-effector (tip) of the robot, where
the users’ hand must be positioned. Each DOF is driven by a brushless DC motor
incorporated with a harmonic drive; each motor has a Hall Effect sensor used for position
feedback of the joints. A backplane card collects analog and digital signals and connects
through the proper interface cards to an NI PXI-7813R (Reconfigurable Input-Output card)
placed on an NI PXI-1031 chassis. The card has an integrated FPGA in which is executed the
low-level control: A PI controller for the current loop of the motors, position feedback via the
Hall Effect sensors and the collection of the force sensor inputs. In the chassis is also
mounted a PXI-8108 controller, which executes the high-level control: the robot operating
system and the trajectory tracking controller. The force-position control is implemented with
an update rate of 1ms.
A PC runs the virtual environment that is the human-machine interface in which the robot
user visualizes the rehabilitation exercise. Security is a major concern. Hardware stoppers
keep the range of motion in secure extent, software position and velocity limits stop the
motor outputs if exceeded, and the system has a hardware emergency stop button, accessible
anytime to the user.
For the following test, the perturbation observed was characterized using the force sensor of
the robot. The main diagonals of the gain matrices, leaving the remaining elements in cero,
were: = [20202020202020] and = [100100100100100100100] and = [1122111] .
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Figure 4.2 Subject wearing ETS-MARSE robot arm and virtual interface
4.3.2 Joint space task
The tests in this scenario were conducted with three healthy male subjects in seated position,
ages 27-34 years old, weight between 78 to 91 kg and height 179-182 cm. The subjects were
requested to perform two joint movements; the first one consisted of the extension and
flexion of the elbow joint (joint 4 on ETS-MARSE) followed by the external and internal
rotation of the shoulder joint (joint 3 on ETS-MARSE). Two repetitions of the sequence were
performed. The motion is illustrated in Figure 4.3; the left-side graphic shows the elbow
movement and the right-side one the shoulder movement. The subjects were trained to
perform an external-internal rotation of between 0 degrees and 50 degrees at joint 3, and an
extension-flexion of between 90 degrees and 20 degrees at joint 4, staying close to 5 seconds
in each part of the movement. Since this is an active rehabilitation exercise, the robot doesn’t
control the amplitude or the speed of the exercise. Figure 4.4 displays one subject’s results.
The upper-row plots show the force estimated by the observer after filtering. The force is
filtered to avoid perceptible oscillations for the subject; this can also be achieved by adding a
damping term to the admittance function. The left plot corresponds to joint 3 (shoulder
external-internal rotation) and the right one to joint 4 (elbow extension-flexion). The
movement of the joints is illustrated on the bottom-row plots that represent the position of the
corresponding joints in time.
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Figure 4.3 Joint space exercises
Figure 4.4 Joint space exercise estimated torques and joint positions
It is important to mention that the precision of the estimation of the torque magnitude is not a
critical point in the proposed method. That is also why the simplification shown in (4.11) is
valid for this approach. Estimating the torque acting on the joints by the effect of the human
interaction allows us to detect the subject’s movement intentions and command the robot to
follow that movement.
It is then possible to change the gain of the estimated torque in order to make the system
more or less sensitive to this perturbation. Indeed, variation in the admittance coefficients
(spring constant) will cause variation in the resistance needed to move the exoskeleton
(virtual spring effect). Using this concept, the rehabilitation exercise can be executed with
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different compliances. This will translate into more or less effort for the user to move the
robot.
Figure 4.5 Joint 3 position and estimated and measured force for joint space test
To illustrate this behavior, the second exercise of this scenario is focused on one joint (joint
3). The subjects were requested to perform an external-internal rotation of the shoulder (as
shown on the right side of Figure 4.3); then, during the same test, the value of the joint
estimation gain was reduced in real-time and the user repeated the movement. In Figure 4.5,
the real-time position of joint 3 is shown in the top plot, and in the bottom one, the external
torque for one of the users. For reference, the reading of a 6DOF force sensor mounted on the
base of the ETS-MARSE’s handle (see Figure 4.2) is shown. The force sensor reading is
presented in a solid line and the estimation of the observer is shown in the dotted line. It is
clear that changing the gain in the observer (vertical line at approximately 27 seconds)
doesn’t impede on estimating the subject’s movement intention. However, it is evident how
the robot’s movement amplitude changed between the first movement and the two
subsequent ones, once the gain was changed. The force sensor reading shows how, although
the external torque exerted by the user in all the cases is approximately the same, the
estimation changes. Thus, with the same force, the subject produced a greater range
movement; or it can also be said that with the initial gain, more effort was needed to achieve
the same movement amplitude as for the last two movements. With these results, the
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objective of using the force observer in combination with the admittance function to perform
isokinetic exercises is demonstrated.
4.3.3 Cartesian space task
For the Cartesian space scenario, the subject was requested to follow a straight line in the
virtual interface. The objective of this test was to evaluate the performance of the robot under
a coordinated multi-joint movement representing a common active rehabilitation task. In this
case, joints 2, 3 and 4 of the robot are allowed to move simultaneously. This test was
performed with a healthy male subject, 33 years old, 98 kilograms weight, and 182 cm height
in seated position. The coordinates of the straight line are expressed in the inertial frame of
reference (refer to Figure 4.1). The result of this test is shown in Figure 4.6. It can be seen
that the user can successfully perform the exercise. As usual in robot rehabilitation, the
tracking of the test can be recorded and serve as a reference for the subject’s improvement or
as mentioned before, the effort required from the user to move may be improved in order to
make the rehabilitation exercise more demanding.
Figure 4.6 Cartesian space trajectory test results
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Varying the trajectory to be followed and the joints involved in the movement significantly
affects the force estimation. The nonlinear observer must be calibrated for different positions;
thus, it will be necessary, in future work, to implement the dynamic adjustment of its
parameters according to the arm configuration.
Finally, in order to experimentally validate the behavior of the nonlinear observer, Figure 4.7
shows the behavior of the state variable compared against the measured position. The test
followed the movements described in Figure 4.3; it consisted on an elbow extension/flexion
and a shoulder external/internal rotation. The right column shows information of joint 3
(shoulder external/internal rotation) and the left one of joint 4 (elbow extension/flexion). It
can be seen in the upper plots that the measured position and estimated position overlaps. In
order to better compare the real and estimated state the estimation error is shown in
the lower plots.
Figure 4.7 Measured and estimated position and position error
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4.4 Conclusions
This paper successfully shows that a force observer can be used as an alternative to force
sensors, in order to perform some active rehabilitation tasks. This advantage allows applying
force directly to the robot structure, theoretically without restrictions, since patients with high
spasticity can easily damage a force sensor.
Some considerations need to be taken into account. A force should be detected continuously;
otherwise, the estimation will go to zero intermittently causing the robot to stop-and-go
erratically; consequently, the robot should constantly present minimal (adjustable) opposition
to the movement. Therefore, having a completely compliant system is not adequate for this
approach unless this behavior is resolved. Hence, the importance of using the proposed
method to perform resistive rehabilitation exercises (isokinetic).
A more accurate model of the robot will result in better estimation of interactive forces;
nevertheless, a complete model of a robot with high degree-of-freedom is computationally
heavy. This approach consumes much more resources than processing a force sensor input.
There is also a critical issue that must be addressed in order to improve this approach. As
shown, when the exercises are aimed at a specific joint or sequence, the estimation of the
force can be used directly. Nevertheless, as the movements become more complex, a greater
complexity arises in determining the ergonomic position of the redundant robot. A solution
for these cases is necessary in order to employ the robot for a wide variety of movements.
DISCUSSION OF THE RESULTS
The work presented in this thesis describes the design and implementation of a control
strategy for the ETS-MARSE robot, as well as the design of active-assistive rehabilitation
and active rehabilitation strategies. Moreover, passive rehabilitation is possible with the
presented control law. In all rehabilitation cases (passive, active-assisted and active), some
Cartesian trajectories are possible to execute according to the rehabilitation task pursued.
To achieve the described results, the methodology presented in Chapter 1 was followed. In
the matter of the control technique, using VDC allowed to have robustness against changes in
the robot’s user characteristics. Thus, the rehabilitation provided can be more systematic and
the variations depend almost completely on the patients’ improvement. Passive and active
rehabilitation exercises were implemented both in joint and in Cartesian space. A
performance evaluation using the VDC approach against CTC and PID was presented,
supporting the better performance of VDC. Also the simplification of the dynamical model of
the robot through the virtual decomposition presented an advantage.
About the sensing interface, addressed in Chapter 3 and Chapter 4 of this thesis, different
rehabilitation schemes were proposed for active-assistive and active rehabilitation task with
the guidance of the ETS-MARSE. The rehabilitation schemes were basically presented in
Chapter 3, in which was demonstrated that our robot is able to vary the assistance provided to
future rehabilitation patients. The amount of variation of the trajectory can be quantified as
an excellent measurement of progression of the subject. Also, the robot can perform a free
movement according to the user intention of motion. The ETS-MARSE will help him to
accomplish the task only when is required by the exercise specifications (virtual wall limits),
letting the subject control the free motion in any other moment. At the same time, the robot
will be providing help in gravity compensation; for the robot itself by default and for the
patients’ arm if necessary. Finally, in Chapter 4, it was shown that a force observer can be
used instead of a force sensor for certain tasks. To recognize the subject’s intended
movement, it is not necessary a precise measurement of the force, a close estimate is
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sufficient. This method allows reducing the dependency of a force sensor that can easily be
damaged by the patient’s condition.
CONCLUSION
This thesis work was focused on obtaining a consistent control technique for the ETS-
MARSE (Motion Assistive Robotic-exoskeleton for Superior Extremity) and to obtain a
reliable sensing interface that could capture the user intention of movement to provide
different assisted and active-assisted rehabilitation techniques.
With the results presented in this work, different rehabilitation schemes and characteristics
are offered. It is safe to say that the robot has a reliable control strategy as well as
rehabilitation-task capabilities. Although investigation in the field of control and increasing
the tasks that the exoskeleton can perform is always interesting and an area of many
opportunities, the current developments need to be consolidated for the next phase of the
robot. The ETS-MARSE is ready to move from a development environment to a test
environment, with the pertinent considerations listed next in the recommendations section.
RECOMMENDATIONS
In order to continue the development of this project to fulfill the final aim of having a robotic
prototype to be used in rehabilitation and possibly daily assistance, some considerations need
to be made:
The advances so far (different modes of passive rehabilitation, active-assisted rehabilitation,
active rehabilitation, the human-machine interface, between others) had been developed and
tested with healthy human beings. An important next step is to start the validation of the
techniques in trials with rehabilitation patients. To precede with this step a profound safety
review is necessary.
Another important step in order to achieve full usability of the rehabilitation strategies is the
development of a complete solution for the robot inverse kinematics problem. That is, the
exoskeleton can reach some points of its workspace in more than one configuration of its
links (redundancy). Solving this redundancy problem, will give complete ranges in
admittance and Cartesian space trajectories.
As the next step for active rehabilitation, the use of electromyographic signals is a promising
objective. EMG signals can be combined with force sensor readings or force observer
estimations in order to provide a more detailed interpretation of the subject’s movement
intention. Also can be used alone for subjects in whom the force sensor may be not enough to
determine the intended movement.
Continue to develop the haptic and teleoperation ideas for the ETS-MARSE is an important
area of opportunity. A consolidation of the different modes of operation in the development
environment (LabView) is necessary. The update of the virtual environment of the human-
machine interface is also a mandatory next step to the process of maturation of the project.
APPENDIX A
ELEMENTS IN THE REGRESSOR MATRIX AND PARAMETER VECTOR θA
Non-zero elements in the regressor matrix ∈ ℝ × for the link linear parametrization in
(2.14):
(1,1) = ( )(1) + (5) (3) − (6) (2) + (1) (A A-1)
(1,2) = − (5) (5) − (6) (6) (A A-2)
(1,3) = − ( )(6) + (5) (4) (A A-3)
(1,4) = ( )(5) + (6) (4) (A A-4)
(2,1) = ( )(2) + (6) (1) − (4) (3) + (2) (A A-5)
(2,2) = ( )(6) + (4) (5) (A A-6)
(2,3) = − (4) (4) + (6) (5) (A A-7)
(2,4) = − ( )(4) + (6) (5) (A A-8)
(3,1) = ( )(3) + (4) (2) − (5) (1) + (3) (A A-9)
(3,2) = − ( )(5) + (4) (6) (A A-10)
(3,3) = ( )(4) + (5) (6) (A A-11)
(3,4) = − (4) (4) − (5) (5) (A A-12)
(4,3) = (3,1) (A A-13)
(4,4) = − (2,1) (A A-14)
(4,6) = (3,3) (A A-15)
(4,7) = − (2,4) (A A-16)
(4,8) = (3,2) (A A-17)
(4,9) = − (2,2) (A A-18)
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(4,10) = (6) (6) − (5) (5) (A A-19)
(4,11) = ( )(4) + (5) (6) − (6) (5) (A A-20)
(4,12) = − (6) (5) (A A-21)
(4,13) = (5) (6) (A A-22)
(5,2) = − (3,1) (A A-23)
(5,4) = (1,1) (A A-24)
(5,5) = − (3,2) (A A-25)
(5,7) = (1,4) (A A-26)
(5,8) = − (3,3) (A A-27)
(5,9) = (4) (4) − (6) (6) (A A-28)
(5,10) = (1,3) (A A-29)
(5,11) = (6) (4) (A A-30)
(5,12) = ( )(5) + (6) (4) − (4) (6) (A A-31)
(5,13) = − (4) (6) (A A-32)
(6,2) = (2,1) (A A-33)
(6,3) = − (1,1) (A A-34)
(6,5) = (2,2) (A A-35)
(6,6) = − (1,3) (A A-36)
(6,8) = (5) (5) − (4) (4) (A A-37)
(6,9) = (2,4) (A A-38)
(6,10) = − (1,4) (A A-39)
(6,11) = − (5) (4) (A A-40)
(6,12) = (4) (5) (A A-41)
(6,13) = ( )(6) + (4) (5) − (5) (4) (A A-42)
The 13 elements of parameter vectors ℝ are listed as:
= (A A-43)
= (A A-44)
105
= (A A-45)
= (A A-46)
= (A A-47)
= (A A-48)
= (A A-49)
= − (A A-50)
= − (A A-51)
= − (A A-52)
= (A A-53)
= (A A-54)
= (A A-55)
where is the mass; = , , ∈ ℝ denotes a vector pointing from the
origin of frame towards the mass centre, expressed in frame ; and , , , , , are the elements of .
APPENDIX B
MOTORS AND HARMONIC DRIVES SPECIFICATIONS
Table-A B-1 ETS-MARSE detailed specification for DC motors and harmonic drives
Actuators, Maxon brushless DC motors
Specification EC-90, flat 90 W
(joints 1, 2, 4)
EC-45, flat 30 W
(joints 3, 5–7)
Nominal voltage (V) 24 12
Nominal speed (rpm) 2650 2860
Torque constant (mNm/A) 70.5 25.5
Weight (g) 648 88
Harmonic drives
Specification CSF-2UH17–120 F
(joints 1, 2)
CSF-2XH14–100 F
(joint 4)
CSF-2XH11–100 F
(joints 3, 5–7)
Torque at 2000 rpm (Nm) 24 7.8 5
Momentary peak torque (Nm) 86 54 25
Repeated peak torque (Nm) 54 28 11
Gear ratio 120 100 100
ANNEX I
ADITIONAL AND FUTURE WORK: ELECTROMYOGRAPHY, TELEOPERATION AND HAPTIC CAPABILITIES
The present annex describes additional work realized with the ETS-MARSE that led to the
publication of other articles with the research group. The first section describes the first
advances in EMG signal processing for commanding the mentioned exoskeleton. The content
is presented as a straightforward report, with only a briefly overview of the problem and the
general specifications of the technique used. For specific information about the application
proposed, the reader should refer to the papers cited in the text. The second section briefly
describes the work in the area of teleoperation of the ETS-MARSE.
A I - 1. Electromyography
We can define electromyography as a technique for evaluating and recording the electrical
activity produced by skeletal muscles (Robertson, 2004). In general, the muscles are the
actuators responsible of human motion; at a very basic approach, in normal conditions, the
muscle contractions are activated by the cortex and transmitted by the nervous systems to
reach the muscular tissue. The use of EMG signals to control exoskeleton robots have been in
constant development in the present century (Khokhar, Xiao and Menon, 2010; Komada et
al., 2009; Lucas, DiCicco and Matsuoka, 2004; Rosen et al., 2001). There are two kinds of
EMG signals that can be collected: surface signals or intramuscular signals; being the second
one an invasive method. In our project we work with surface EMG signals. There are three
basic steps to use EMG signals in any task, illustrated in Figure A-I.1:
Figure-A I-1 Basic steps of EMG signal processing
Signal detection (sensing, amplifying
and filtering)Signal processing Signal classification
(control)
110
The first step is to detect or sense the EMG signals from the muscles, where the activity is
measured, amplified and filtered. The raw EMG signals come with lot of noise and do not
have ready-to-use information. Hence, as a second step is necessary to perform processing of
the signal to extract more meaningful information.
The second step is the feature detection or extraction of the EMG signals by means of which,
certain information closely related with the muscular activity can be obtained. The signal can
be analyzed in time domain, where the signal is usually first rectified and then analyzed with
some techniques as linear envelope, root mean square (RMS), Willison amplitude (Smith et
al., 2008), among others; or in frequency domain, with methods like spectral analysis of
random signals, mean frequency and median frequency. Recently there are some interesting
works that are achieving good results like using wavelet transform (Jiang et al., 2005) that
also can be used in the detection phase (Phinyomark, Limsakul and Phukpattaranont, 2010)
and particle swarm optimization (Khushaba, Al-Ani and Al-Jumaily, 2007).
Finally, the classification of the signals needs to be done in order to generate a desired
control action. EMG signals are highly nonlinear and vary from one subject to another, even
for the same movement. The signals also depend on the subject’s physiological condition
(stress, exhaustion, attention, etc.), also can fluctuate due to factors such as sweating, small
changes in the positioning of the electrodes, arm position, and others.This step can go from
basic methods like simple threshold or double threshold, to complex pattern recognition
algorithms.
In our project, in order to perform the signal detection (first step), the Bagnoli-16 Main
Amplifier Unit along with its input modules and Single Differential Surface EMG Sensors,
from DELSYS® were used. The signals are collected through the backplane card described
in subsections 2.4 or subsection 3.2, and sent to the NI PXI-8081 through the NI PXI-7813R
input/output card, both also described in the mentioned subsections. The configuration of the
voltage range of the raw EMG signals is ±5V.
111
For the second step, the signal processing, for this first stage of development were considered
different basic filtering techniques as RMS, mean of the absolute value, moving average, and
Savitzky-Golay (Savitzky and Golay, 1964). The RMS filtering (a measure of power of the
signals) shows for our case the best performance, having a very small delay in the signal
processing. The RMS filtering is defined as follows:
= 1
(A I-1)
where is the voltage of the th sample of the EMG signal and N is the number of samples.
In our experiment, the number of samples was set to 50 with a sampling time of 0.5ms. An
example of the RMS filtering is shown in Figure A-I.2, the left plot shows the raw EMG
signal and the right one, the filtered signal.
Figure-A I-2 Example of raw EMG signals and RMS value
For the final step of executing a control action with the filtered EMG signal, an approach is
proposed in which agonist and antagonist muscle groups are used (as biceps for elbow
flexion and triceps for elbow extension). The EMG signals processed from these groups of
muscles are used as virtual force/torque applied to the corresponding joint they drive, through
0 1 2 3 4 5-0.6
0
0.4
Time (s)
EMG
(mV
)
0 1 2 3 4 5-0.05
0
0.15
Time (s)
RM
S (m
V)
112
a proportional constant. The results presented in the paper (Rahman et al., 2015a) shows the
results of the presented approach.
Besides the mentioned paper, the EMG processing is used along with the force based control
(FBC) described in Chapter 3 to analyze the effectiveness of the force control approach
presented (Rahman et al., 2014).
As another use of the EMG signal processing, a neuro-fuzzy controller is being developed. A
neuro-fuzzy controller can be trained to adapt to different users and different motion
situations. Using the flexible and adaptable nature of this controller, it is expected to develop
an effective knowledge base that can overcome aforementioned problems of an EMG based
control (EBC). So far, an elementary fuzzy controller for the elbow has been tested with the
first satisfactory results. In the developing process, the ETS-MARSE can be used in any of
the operation modes described in this thesis (passive, active-assistive and active) to generate
a motion database and use an Adaptive Neuro-Fuzzy Inference Systems (ANFIS) to generate
the equivalent fuzzy inference system. The work so far in this area is in its initial state and a
lot of work is necessary for the first functional rehabilitation schemes with EBC or a
FBC/EBC hybrid.
A I - 2. Teleoperation and haptic capabilities
Teleoperation is an extensive area in robotics. It spans from simple remote controlled
devices, to exploration robots of other planets. In the case of medical robots and devices,
teleoperation has given the opportunity to perform successful remote surgeries in which
haptic capabilities of the robot have played also a vital role. In the case of tele-diagnostics of
physiological conditions, some devices are able to use image processing to read and
diagnose, with the guide of specialists, some conditions that restrain human natural motion.
Teleoperation is an option that can present an opportunity to overcome the same problem of
insufficient number of qualified therapist that can perform rehabilitation processes in site.
113
For our device, we are proposing teleoperation capabilities that will allow the generation of
predefined rehabilitation exercise in a remote way, as well as real time maneuvering of the
subject that wears the exoskeleton with haptic feedback of the patient condition and
evolution. To give the ETS-MARSE these capabilities a master-slave device was used first.
The second step in developing of teleoperation capabilities uses the PHANTOM Omni®
haptic device from Sensable® Technologies, a 6DOF positional sensing device compact and
portable, with two integrated switches (buttons) that add more customization capabilities. So
far, it has been developed an interface in which the user is able to select different points in
the Phantom workspace and they are sent to the ETS-MARSE via UDP communication for it
to perform, mapped to its own workspace, the same trajectory defined by the haptic device.
These trajectories are consequently defined in the Cartesian space and can include any
number of via points. Real time trajectory tracking and haptic capabilities are to be
incorporated to this approach. A virtual environment for full feedback has started to be
developed.
ANNEX II
VIRTUAL DECOMPOSITION CONTROL
This annex presents a more general description of VDC control. The information presented in
the papers part of this thesis is specific for the application in our robot. However the
technique can be extended easily. Some generalities are briefly described next according to
(Zhu, 2010). This annex covers only the application for manipulator-like robots; however
VDC can be applied for space robots (no gravity), humanoid robots, force-reflected bilateral
teleoperation, and modular robot manipulators. The VDC approach can also be extended to
distributed parameter systems and to electrical circuits.
A II - 1 Subsystem decomposition and kinematics
First, the reference frames of the robot are established. Decomposition is done by placing
virtual cutting points that separate each joint and link of the system into a subsystem. The
Denavit-Hartenberg parameters or the modified Denavit-Hartenberg parameters are obtained
in order to obtain the homogeneous transformation matrices of the system. Using these
matrices and defining any pair of frames { } and{ }, the force/moment transformation
matrices are calculated as follows:
= 0 ×( ×) ∈ ℝ × (A II-1)
where represents the rotation matrix from one frame to the next one and the
distance between them, and:
( ×) = 0 − (3) (2)(3) 0 − (1)− (2) (1) 0
(A II-2)
116
where ( ) represents the term of the vector. Each force/moment transformation
matrix for = 1,… , − 1. The next step is to calculate , the linear/angular
velocity vectors of the { } frames for = 1,… , as follows:
= ∈ ℝ (A II-3)
where is the linear velocity vector and is the angular velocity vector of the
corresponding frame. Defining each joint position (angle) as to and using the previous
linear/angular velocity vectors in (A II-3), the augmented velocity vector is formed with the
following form:
= [ ⋯ ⋯ ] (A II-4)
Factorizing the joint velocity vector in (A II-4) it is obtained:
= (A II-5)
where = [ ⋯ ] is the joint velocity vector and is the 49 × VDC Jacobian
matrix of the system:
= 0 ⋯ 0 ⋱ ⋮⋮ ⋱ ⋱ 0 …
(A II-6)
where = [0 0 0 0 0 1] , represents the × identity matrix and 0 is a six
element zero vector. Finally, for the kinematics it is necessary to calculate the required
velocities, which are a function of the control requirements.
117
= + ( − ) (A II-7)
where = [ ⋯ ] is the required velocity vector, = [ ⋯ ] is the
desired velocity vector, > 0 is a control parameter, = [ ⋯ ] is the desired
position vector and = [ ⋯ ] the position vector. From (A II-6) and (A II-7) the
augmented required velocity vector is obtained as follows:
= (A II-8)
From (A II-4) can be established:
= [ ⋯ ⋯ ] (A II-9)
A II-2 Dynamics
To obtain the inverse dynamics that takes part in the control of the robot, it is necessary to
calculate the required force/moment vectors for the links, , and then the net torques
required by the joints, ∗ . The first step for the link dynamics is to obtain the required net
force/moment vectors with the following equation:
∗ = + ( − ) (A II-10)
For = 1,… , where ∗ are the required net force/moment vectors, is a symmetric
positive-definite gain matrix, and are the velocities defined in (4) and (9). ∈ℝ × is a regressor matrix composed by elements of / ( ) ∈ ℝ , the velocity
vectors ∈ ℝ and ∈ ℝ , and terms from the vector of gravity propagation, and where ∈ ℝ is the estimated parameters vector composed by the mass of the link, the elements
of the vector pointing from the origin of the reference frame of the link toward its mass
center, and elements of the inertia tensor of the link. To estimate the parameters in , is
defined as follows:
118
= ( − ) (A II-11)
= ( ), , ( ), ( ), (A II-12)
For = 1,… , and = 1,… ,13where represents the th parameter of the th joint, ( ) ∈ ℝ is a scalar variable, is the parameter update gain, ( ) and ( ) are the
lower and upper bounds of respectively, and the projection function , is a differentiable
scalar function defined for ≥ 0 such that its time derivative is governed by:
= ( ) (A II-13)
with:
= 001 ≤ ( ) ( ) ≤ 0 ≥ ( ) ( ) ≥ 0ℎ
Once this step is done, the required force/moment vectors at the cutting points are obtained as
follows:
= ∗ = ∗ + (A II-14)
for = − 1,… ,1. The next step is the calculation of the dynamics of the joints. For = 1,… , in (A II-15), (A II-16), (A II-17) and (A II-18), the following vector and
parameter vector are defined:
= [ ( ) 1] (A II-15)
= [ ] (A II-16)
119
where the sub-index in the vectors is used to differentiate joint variables form the link
variables introduced in (A II-10), is the equivalent mass or moment of inertia, > 0
denotes the Coulomb friction coefficient, > 0 the viscous friction coefficient and
denotes an offset that accommodates asymmetric Coulomb frictions. Defining the function:
= ( − ) (A II-17)
Then, the same procedure as above in (A II-12) and (A II-13) is used to estimate the
parameters. Next the net torque for the joint ∗ is obtained as follows:
∗ = + ( − ) (A II-18)
where ∗ is the net torque of the joint, denotes a feedback gain and ∈ ℝ denotes the
estimate of ∈ ℝ .
A II-3 Control
To develop the control of the entire system, the torque resulting from the link and joint
analysis are combined. First, it is required to extract the torque of the link force/moment
vector.
= (A II-19)
for = 1,… , . With = [0 0 0 0 0 1] that was defined before, the control torque
is designed as:
= ∗ + (A II-20)
for = 1,… , .
BIBLIOGRAPHY
Alcocer, A., A. Robertsson, A. Valera and R. Johansson. 2003. « Force estimation and control in robot manipulators ». In Robot Control 2003 (SYROCO'03): A Proceedings Volume from the 7th IFAC Symposium, Wrocław, Poland, 1-3 September 2003. (1-3 September 2003) Vol. 1, p. 55. International Federation of Automatic Control.
Artemiadis, Panagiotis K., and Kostas J. Kyriakopoulos. 2008. « Estimating arm motion and
force using EMG signals: On the control of exoskeletons ». In 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2008). (Nice, France, 22-26 September), p. 279-284.
Asada, Haruhiko, and Jean-Jacques E Slotine. 1986. Robot analysis and control. New York:
J. Wiley, 277 p.
Brackbill, E. A., Mao Ying, S. K. Agrawal, M. Annapragada and V. N. Dubey. 2009.
« Dynamics and control of a 4-dof wearable cable-driven upper arm exoskeleton ». In Robotics and Automation, 2009. ICRA '09. IEEE International Conference on. (12-17 May 2009), p. 2300-2305.
Brigham and Women’s Hospital Rehabilitation Services. 2014. « Physical Therapy Standards
of Care and Protocols ». < http://www.brighamandwomens.org/Patients_Visitors/pcs/rehabilitationservices/ StandardsofCare.aspx >. Accessed 2 September 2014.
Brokaw, Elizabeth B., Theresa Murray, Tobias Nef and Peter S. Lum. 2011. « Retraining of
interjoint arm coordination after stroke using robot-assisted time-independent functional training ». Journal of Rehabilitation Research & Development, vol. 48, no 4, p. 299-316.
Bureau of Labor Statistics. 2015. « Occupational Outlook Handbook, 2014-15 Edition,
Physical Therapists ». < http://www.bls.gov/ooh/healthcare/physical-therapists.htm >. Accessed February 26 2015.
Calanca, Andrea, and Paolo Fiorini. 2014. « Human-Adaptive Control of Series Elastic
Actuators ». Robotica, vol. CJO, no First View, p. 1-16.
122
Chan, Linping, Fazel Naghdy and David Stirling. 2013. « Extended active observer for force estimation and disturbance rejection of robotic manipulators ». Robotics and Autonomous Systems, vol. 61, no 12, p. 1277-1287.
Chiri, Azzurra, Nicola Vitiello, Francesco Giovacchini, Stefano Roccella, Fabrizio Vecchi
and Maria Chiara Carrozza. 2012. « Mechatronic Design and Characterization of the Index Finger Module of a Hand Exoskeleton for Post-Stroke Rehabilitation ». IEEE/ASME Transactions on Mechatronics, vol. 17, no 5, p. 884-894.
Ciliz, M. Kemal. 2005. « Adaptive control of robot manipulators with neural network based
compensation of frictional uncertainties ». Robotica, vol. 23, no 02, p. 159-167.
Colombo, Roberto, Fabrizio Pisano, Silvestro Micera, Alessandra Mazzone, Carmen
Delconte, M Chiara Carrozza, Paolo Dario and Giuseppe Minuco. 2005. « Robotic techniques for upper limb evaluation and rehabilitation of stroke patients ». IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 13, no 3, p. 311 - 324.
Coote, Susan, Brendan Murphy, William Harwin and Emma Stokes. 2008. « The effect of
the GENTLE/s robot-mediated therapy system on arm function after stroke ». Clinical Rehabilitation, vol. 22, no 5, p. 395-405.
Craig, John J. 2005. Introduction to robotics: mechanics and control, 3rd. Upper Saddle
River, N.J.: Pearson/Prentice Hall, 408 p.
Culmer, Peter R., Andrew E. Jackson, Sophie Makower, Robert Richardson, J. Alastair
Cozens, Martin C. Levesley and Bipin B. Bhakta. 2010. « A Control Strategy for Upper Limb Robotic Rehabilitation With a Dual Robot System ». IEEE/ASME Transactions on Mechatronics, vol. 15, no 4, p. 575-585.
Department of Economic and Social Affairs. 2013. World Population Ageing 2013.
Coll. « World Population Ageing ». New York: United Nations.
Dipietro, Laura, Mark Ferraro, Jerome Joseph Palazzolo, Hermano Igo Krebs, Bruce T.
Volpe and Neville Hogan. 2005. « Customized interactive robotic treatment for stroke: EMG-triggered therapy ». IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 13, no 3, p. 325-334.
123
Do, K D, and J Pan. 2008. « Nonlinear control of an active heave compensation system ». Ocean Engineering, vol. 35, no 5, p. 558-571.
Eschweiler, Jörg, Kurt Gerlach-Hahn, Arne Jansen-Toy and Steffen Leonhardt. 2014. « A
survey on robotic devices for upper limb rehabilitation ». Journal of neuroengineering and rehabilitation, vol. 11, no 1, p. 3.
Feriančik, Miloslav, and Ondrej Líška. 2014. « Automatic rehabilitation device based on
robot and machine vision ». In 2014 International Conference on Mechatronics and Robotics, Structural Analysis (MEROSTA 2014). (Santorini Island, Greece, 17-21 July 2014), sous la dir. de Mastorakis, Nikos, Kleanthis Psarris, George Vachtsevanos, Philippe Dondon, Valeri Mladenov, Aida Bulucea, Imre Rudas, Olga Martin, Bogdan Epureanu, Cho W Solomon To and Hyung Hee Cho, p. 201-203. Coll. « Advances in Robotics, Mechatronics and Circuits ».
Ferrer, Steven Bruce, Cristobal Ochoa-Luna, Mohammad Habibur Rahman, Maarouf Saad
and Philippe S Archambault. 2013. « HELIOS: The human machine interface for MARSE robot ». In Human System Interaction (HSI), 2013 The 6th International Conference on. (6-8 June 2013), p. 117-122.
Frisoli, A., C. Loconsole, D. Leonardis, F. Banno, M. Barsotti, C. Chisari and M.
Bergamasco. 2012. « A New Gaze-BCI-Driven Control of an Upper Limb Exoskeleton for Rehabilitation in Real-World Tasks ». Systems, Man, and Cybernetics, Part C: Applications and Reviews, IEEE Transactions on, vol. 42, no 6, p. 1169-1179.
Garrec, P., J. P. Friconneau, Y. Measson and Y. Perrot. 2008. « ABLE, an innovative
transparent exoskeleton for the upper-limb ». In IEEE/RSJ International Conference on Intelligent Robots and Systems, 2008. IROS 2008. (22-26 September 2008), p. 1483-1488.
Garrec, Philippe. 2010. « Design of an anthropomorphic upper limb exoskeleton actuated by
ball-screws and cables ». University" Politehnica" of Bucharest Scientific Bulletin, Series D: Mechanical Engineering, vol. 72, no 2, p. 23-34.
Gopura, R. A. R. C., and K. Kiguchi. 2007. « Development of an exoskeleton robot for
human wrist and forearm motion assist ». In Industrial and Information Systems, 2007. ICIIS 2007. International Conference on. p. 535-540.
124
Gorinevsky, Dimitry M., Alexander M. Formalsky and Anatoly Yu Schneider. 1997. Force control of robotics systems. Boca Raton, FL: CRC Press, 363 p.
Gupta, Abhishek, and Marcia K. O'Malley. 2006. « Design of a haptic arm exoskeleton for
training and rehabilitation ». IEEE/ASME Transactions on Mechatronics, vol. 11, no 3, p. 280-289.
Gupta, Abhishek, and Marcia K O’Malley. 2011. « Disturbance-observer-based force
estimation for haptic feedback ». Journal of Dynamic Systems, Measurement, and Control, vol. 133, no 1, p. 014505.
Gupta, Neeru, Carla Castillo-Laborde and Michel Landry. 2011. « Health-related
rehabilitation services: assessing the global supply of and need for human resources ». BMC Health Services Research, vol. 11, no 1, p. 276.
Hacksel, P. J., and S. E. Salcudean. 1994. « Estimation of environment forces and rigid-body
velocities using observers ». In 1994 IEEE International Conference on Robotics and Automation. p. 931-936. IEEE.
He, W., Y. Zhao, H. Tang, C. Sun and W. Fu. 2015. « A Wireless BCI and BMI System for
Wearable Robots ». Systems, Man, and Cybernetics: Systems, IEEE Transactions on, vol. PP, no 99, p. 1-11.
Health Canada. 2006. « It's Your Health - Stroke ». < http://www.hc-sc.gc.ca/hl-vs/iyh-
vsv/diseases-maladies/stroke-vasculaire-eng.php >. Accessed 22 September 2015.
Hesse, Stefan, Henning Schmidt and Cordula Werner. 2006. « Machines to support motor
rehabilitation after stroke: 10 years of experience in Berlin ». Journal of Rehabilitation Research & Development, vol. 43, no 5, p. 671-678.
Hu, X. L., K. Y. Tong, R. Song, X. J. Zheng and K. H. Lui. 2008. « Robot-assisted wrist
training for chronic stroke: A comparison between electromyography (EMG) driven robot and passive motion ». In Biomedical Robotics and Biomechatronics, 2008. BioRob 2008. 2nd IEEE RAS & EMBS International Conference on. (19-22 October 2008), p. 637-641.
Hu, X. L., K. Y. Tong, R. Song, X. J. Zheng, K. H. Lui, W. W. F. Leung, S. Ng and S. S. Y.
Au-Yeung. 2009. « Quantitative evaluation of motor functional recovery process in
125
chronic stroke patients during robot-assisted wrist training ». Journal of Electromyography and Kinesiology, vol. 19, no 4, p. 639-650.
Hu, X. L., K. Y. Tong, X. J. Wei, W. Rong, E. A. Susanto and S. K. Ho. 2013. « The effects
of post-stroke upper-limb training with an electromyography (EMG)-driven hand robot ». Journal of Electromyography and Kinesiology, vol. 23, no 5, p. 1065-1074.
Hu, Xiaoling, Kai Yu Tong, Rong Song, Vincent S. Tsang, Penny O. Leung and Le Li. 2007.
« Variation of muscle coactivation patterns in chronic stroke during robot-assisted elbow training ». Arch Phys Med Rehabil, vol. 88, p. 1022 - 1029.
Huang, J., X. Tu and J. He. 2015. « Design and Evaluation of the RUPERT Wearable Upper
Extremity Exoskeleton Robot for Clinical and In-Home Therapies ». Systems, Man, and Cybernetics: Systems, IEEE Transactions on, vol. PP, no 99, p. 1-10.
Jackson, A E, R J Holt, P R Culmer, S G Makower, M C Levesley, R C Richardson, J A
Cozens, Mon M Williams and B B Bhakta. 2007. « Dual robot system for upper limb rehabilitation after stroke: the design process ». Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 221, no 7, p. 845-857.
Jiang, M. W., R. C. Wang, J. Z. Wang and D. W. Jin. 2005. « A Method of Recognizing
Finger Motion Using Wavelet Transform of Surface EMG Signal ». In Engineering in Medicine and Biology Society, 2005. IEEE-EMBS 2005. 27th Annual International Conference of the. (17-18 January 2006), p. 2672-2674.
Katsura, S., Y. Matsumoto and K. Ohnishi. 2007. « Modeling of Force Sensing and
Validation of Disturbance Observer for Force Control ». Industrial Electronics, IEEE Transactions on, vol. 54, no 1, p. 530-538.
Kazerooni, H., and Jenhwa Guo. 1993. « Human Extenders ». Journal of Dynamic Systems,
Measurement, and Control, vol. 115, no 2B, p. 281-290.
Khokhar, Z. O., Z. G. Xiao and C. Menon. 2010. « Surface EMG pattern recognition for real-
time control of a wrist exoskeleton ». Biomed Eng Online, vol. 9, p. 41.
Khushaba, Rami N., Ahmed Al-Ani and Adel Al-Jumaily. 2007. « Swarm Intelligence based
Dimensionality Reduction for Myoelectric Control ». In Intelligent Sensors, Sensor
126
Networks and Information, 2007. ISSNIP 2007. 3rd International Conference on. (3-6 December 2007), p. 577-582.
Kiguchi, K., and Y. Hayashi. 2012. « An EMG-Based Control for an Upper-Limb Power-
Assist Exoskeleton Robot ». Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, vol. 42, no 4, p. 1064-1071.
Klamroth-Marganska, Verena, Javier Blanco, Katrin Campen, Armin Curt, Volker Dietz,
Thierry Ettlin, Morena Felder, Bernd Fellinghauer, Marco Guidali, Anja Kollmar, Andreas Luft, Tobias Nef, Corina Schuster-Amft, Werner Stahel and Robert Riener. 2014. « Three-dimensional, task-specific robot therapy of the arm after stroke: a multicentre, parallel-group randomised trial ». The Lancet Neurology, vol. 13, no 2, p. 159-166.
Komada, S., Y. Hashimoto, N. Okuyama, T. Hisada and J. Hirai. 2009. « Development of a
Biofeedback Therapeutic-Exercise-Supporting Manipulator ». IEEE Transactions on Industrial Electronics, vol. 56, no 10, p. 3914-3920.
Krebs, H. I., J. J. Palazzolo, L. Dipietro, M. Ferraro, J. Krol, K. Rannekleiv, B. T. Volpe and
N. Hogan. 2003. « Rehabilitation Robotics: Performance-Based Progressive Robot-Assisted Therapy ». Autonomous Robots, vol. 15, no 1, p. 7-20.
Krebs, H. I., B. T. Volpe, D. Williams, J. Celestino, S. K. Charles, D. Lynch and N. Hogan.
2007. « Robot-Aided Neurorehabilitation: A Robot for Wrist Rehabilitation ». Neural Systems and Rehabilitation Engineering, IEEE Transactions on, vol. 15, no 3, p. 327-335.
Kurnicki, Adam, Bartłomiej Stanczyk and Bartosz Kania. 2014. « Manipulator development
for telediagnostics ». In 2014 International Conference on Mechatronics and Robotics, Structural Analysis (MEROSTA 2014). (Santorini Island, Greece, 17-21 July 2014), sous la dir. de Mastorakis, Nikos, Kleanthis Psarris, George Vachtsevanos, Philippe Dondon, Valeri Mladenov, Aida Bulucea, Imre Rudas, Olga Martin, Bogdan Epureanu, Cho W Solomon To and Hyung Hee Cho, p. 214-218. Coll. « Advances in Robotics, Mechatronics and Circuits ».
Kwakkel, Gert, Boudewijn J. Kollen and Hermano I. Krebs. 2008. « Effects of Robot-
Assisted Therapy on Upper Limb Recovery After Stroke: A Systematic Review ». Neurorehabilitation and Neural Repair, vol. 22, no 2, p. 111-121.
127
Landry, Michel D, Thomas C Ricketts and Molly C Verrier. 2007. « The precarious supply of physical therapists across Canada: exploring national trends in health human resources (1991 to 2005) ». Human Resources for Health, vol. 5, no 1, p. 23.
Li, Z., S. S. Ge, M. Adams and W. S. Wijesoma. 2008. « Robust adaptive control of
uncertain force/motion constrained nonholonomic mobile manipulators ». Automatica, vol. 44, no 3, p. 776-784.
Lo, Ho Shing, and Sheng Quan Xie. 2012. « Exoskeleton robots for upper-limb
rehabilitation: State of the art and future prospects ». Medical Engineering & Physics, vol. 34, no 3, p. 261-268.
Loureiro, Rui, Farshid Amirabdollahian, Michael Topping, Bart Driessen and William
Harwin. 2003. « Upper Limb Robot Mediated Stroke Therapy—GENTLE/s Approach ». Autonomous Robots, vol. 15, no 1, p. 35-51.
Lucas, L., M. DiCicco and Y Matsuoka. 2004. « An EMG-Controlled Hand Exoskeleton for
Natural Pinching ». Journal of Robotics and Mechatronics, vol. 16, no 5, p. 482-488.
Lum, Peter S., Charles G. Burgar, Peggy C. Shor, Matra Majmundar and Machiel Van der
Loos. 2002. « Robot-assisted movement training compared with conventional therapy techniques for the rehabilitation of upper-limb motor function after stroke ». Archives of Physical Medicine and Rehabilitation, vol. 83, no 7, p. 952-959.
Lum, PS, CG Burgar and PC Shor. 2004. « Evidence for improved muscle activation patterns
after retraining of reaching movements with the MIME robotic system in subjects with post-stroke hemiparesis ». IEEE Trans Neural Syst Rehabil Eng, vol. 12, no 2, p. 186 - 194.
Mackay, Judith, and George A. Mensah. 2004. « The Atlas of Heart Disease and Stroke ».
In., p. 112. Geneva, Switzerland: World Health Organization. < http://www.who.int/cardiovascular_diseases/resources/atlas/en/ >.
Masiero, Stefano, Mario Armani and Giulio Rosati. 2011. « Upper-limb robot-assisted
therapy in rehabilitation of acute stroke patients: focused review and results of new randomized controlled trial ». Journal of Rehabilitation Research & Development, vol. 48, no 4, p. 355-366.
128
Masiero, Stefano, Andrea Celia, Giulio Rosati and Mario Armani. 2007. « Robotic-Assisted Rehabilitation of the Upper Limb After Acute Stroke ». Archives of Physical Medicine and Rehabilitation, vol. 88, no 2, p. 142-149.
Miller, Levi Makaio, and Jacob Rosen. 2010. « Comparison of multi-sensor admittance
control in joint space and task space for a seven degree of freedom upper limb exoskeleton ». In Biomedical Robotics and Biomechatronics (BioRob), 2010 3rd IEEE RAS and EMBS International Conference on. (Tokyo, Japan, 26-29 September 2010), p. 70-75.
Mistry, M., P. Mohajerian and S. Schaal. 2005. « An exoskeleton robot for human arm
movement study ». In Intelligent Robots and Systems, 2005. (IROS 2005). 2005 IEEE/RSJ International Conference on. p. 4071-4076.
National Stroke Association®. 2012. « Effects of Stroke - Paralysis ». Internet.
< http://www.stroke.org/site/PageServer?pagename=paralysis >. Accessed 10 June 2014.
Nef, Tobias, Marco Guidali, Verena Klamroth-Marganska and Robert Riener. 2009.
« ARMin - Exoskeleton Robot for Stroke Rehabilitation ». In World Congress on Medical Physics and Biomedical Engineering, September 7 - 12, 2009, Munich, Germany, sous la dir. de Dössel, Olaf, and WolfgangC Schlegel. Vol. 25/9, p. 127-130. Coll. « IFMBE Proceedings »: Springer Berlin Heidelberg.
Nicosia, S, and P Tomei. 1990. « Robot control by using only joint position measurements ».
Automatic Control, IEEE Transactions on, vol. 35, no 9, p. 1058-1061.
Norouzi-Gheidari, Nahid, Philippe S. Archambault and Joyce Fung. 2012. « Effects of robot-
assisted therapy on stroke rehabilitation in upper limbs: systematic review and meta-analysis of the literature ». Journal of Rehabilitation Research & Development, vol. 49, no 4, p. 479-496.
Ochoa Luna, Cristóbal, Mohammad Habibur Rahman, Maarouf Saad and Philippe S
Archambault. 2014a. « Robotic assisted trajectory tracking for human arm rehabilitation ». In 2014 International Conference on Mechatronics and Robotics, Structural Analysis (MEROSTA 2014). (Santorini Island, Greece, 17-21 July 2014), under the direction of Mastorakis, Nikos, Kleanthis Psarris, George Vachtsevanos, Philippe Dondon, Valeri Mladenov, Aida Bulucea, Imre Rudas, Olga Martin, Bogdan Epureanu, Cho W Solomon To and Hyung Hee Cho, p. 51-55.
129
Ochoa Luna, Cristóbal, Mohammad Habibur Rahman, Maarouf Saad, Philippe S
Archambault and Steven Bruce Ferrer. 2015. « Admittance-based upper limb robotic active and active-assistive rehabilitation ». International Journal of Advanced Robotic Systems, vol. 12, p. 117.
Ochoa Luna, Cristóbal, Mohammad Habibur Rahman, Maarouf Saad, Philippe S
Archambault and Wen-Hong Zhu. 2014b. « Virtual decomposition control of an exoskeleton robot arm ». Robotica, vol. CJO, p. 1-23.
Otten, Alexander, Carsten Voort, Arno Stienen, Ronald Aarts, Edwin van Asseldonk and
Herman van der Kooij. 2015. « LIMPACT:A Hydraulically Powered Self-Aligning Upper Limb Exoskeleton ». IEEE/ASME Transactions on Mechatronics, vol. 20, no 5, p. 2285-2298.
Ozkul, Fatih, and Duygun Erol Barkana. 2013. « Upper-Extremity Rehabilitation Robot
RehabRoby: Methodology, Design, Usability and Validation ». International Journal of Advanced Robotic Systems, vol. 10, p. 1-13.
Patton, James L, Mary Ellen Stoykov, Mark Kovic and Ferdinando A Mussa-Ivaldi. 2006.
« Evaluation of robotic training forces that either enhance or reduce error in chronic hemiparetic stroke survivors ». Experimental Brain Research, vol. 168, no 3, p. 368-383.
Perry, Joel C, and Jacob Rosen. 2006. « Design of a 7 Degree-of-Freedom Upper-Limb
Powered Exoskeleton ». In Biomedical Robotics and Biomechatronics, 2006. BioRob 2006. The First IEEE/RAS-EMBS International Conference on. (20-22 February 2006), p. 805-810.
Perry, Joel C, Jacob Rosen and Stephen Burns. 2007. « Upper-Limb Powered Exoskeleton
Design ». Mechatronics, IEEE/ASME Transactions on, vol. 12, no 4, p. 408-417.
Phinyomark, A., C. Limsakul and P. Phukpattaranont. 2010. « EMG signal estimation based
on adaptive wavelet shrinkage for multifunction myoelectric control ». In Electrical Engineering/Electronics Computer Telecommunications and Information Technology (ECTI-CON), 2010 International Conference on. (19-21 May 2010), p. 322-326.
Pons, José L. (1, 5). 2008. Wearable Robots: Biomechatronic Exoskeletons. Hoboken, N. J.:
Wiley, xviii, 338 p. p.
130
Popescu, N., D. Popescu, M. Ivanescu, D. Popescu, C. Vladu and I. Vladu. 2013. « Force
observer-based control for a rehabilitation hand exoskeleton system ». In Control Conference (ASCC), 2013 9th Asian. (23-26 June 2013), p. 1-6.
Rahman, M. H., T. K. Ouimet, M. Saad, J. P. Kenne and P. S. Archambault. 2011a.
« Dynamic Modeling and Evaluation of a Robotic Exoskeleton for Upper-Limb Rehabilitation ». International Journal of Information Acquisition, vol. 8, no 1, p. 83-102.
Rahman, Mohammad Habibur. 2012. « Development of an exoskeleton robot for UPPER-
LIMB rehabilitation ». Doctor of Philosophy thesis. Montréal, École de technologie supérieure, (xx, 186) p.
Rahman, Mohammad Habibur, Kazuo Kiguchi, Md Mozasser Rahman and Makoto Sasaki.
2006. « Robotic Exoskeleton for Rehabilitation and Motion Assist ». In Industrial and Information Systems, First International Conference on. (8-11 August 2006), p. 241-246.
Rahman, Mohammad Habibur, Thierry Kittel-Ouimet, Maarouf Saad, Jean-Pierre Kenné and
Philippe S Archambault. 2011b. « Dynamic Modeling and Evaluation of a Robotic Exoskeleton for Upper-limb Rehabilitation ». International Journal of Information Acquisition, vol. 8, no 1, p. 83-102.
Rahman, Mohammad Habibur, Thierry Kittel-Ouimet, Maarouf Saad, Jean-Pierre Kenné and
Philippe S. Archambault. 2012a. « Development and Control of a Robotic Exoskeleton for Shoulder, Elbow and Forearm Movement Assistance ». Applied Bionics and Biomechanics, vol. 9, no 2012, p. 275-292.
Rahman, Mohammad Habibur, Cristóbal Ochoa Luna, Mohammad Jahidur Rahman,
Maarouf Saad and Philippe Archambault. 2014. « Force-position control of a robotic exoskeleton to provide upper extremity movement assistance ». International Journal of Modelling, Identification and Control, vol. 21, no 4, p. 390-400.
Rahman, Mohammad Habibur, Cristobal Ochoa Luna, Maarouf Saad and Philippe S
Archambault. 2015a. « EMG Based Control of a Robotic Exoskeleton for Shoulder and Elbow Motion Assist ». Journal of Automation and Control Engineering, vol. 3, no 4, p. 270-276.
131
Rahman, Mohammad Habibur, Mohammad Jahidur Rahman, Cristóbal Ochoa Luna, Maarouf Saad, Jean-Pierre Kenné and Philippe S Archambault. 2015b. « Development of a whole arm wearable robotic exoskeleton for rehabilitation and to assist upper limb movements ». Robotica, vol. 33, no 01, p. 19-39.
Rahman, Mohammad Habibur, Maarouf Saad, Jean-Pierre Kenné and Philippe S
Archambault. 2012b. « Nonlinear Sliding Mode Control Implementation of an Upper Limb Exoskeleton Robot to Provide Passive Rehabilitation Therapy ». In Intelligent Robotics and Applications, sous la dir. de Su, Chun-Yi, Subhash Rakheja and Honghai Liu. Vol. 7507, p. 52-62. Coll. « Lecture Notes in Computer Science », 7507: Springer Berlin Heidelberg.
Rahman, Mohammad Habibur, Maarouf Saad, Jean-Pierre Kenné, Philippe S Archambault
and Thierry Kittel-Ouimet. 2012c. « Development of a 4DoFs exoskeleton robot for passive arm movement assistance ». International Journal of Mechatronics and Automation, vol. 2, no 1, p. 34-50.
Riener, Robert, T Nef and G Colombo. 2005. « Robot-aided neurorehabilitation of the upper
extremities ». Medical & Biological Engineering & Computing, vol. 43, no 1, p. 2-10.
Robertson, D. Gordon E. 2004. Research methods in biomechanics. Champaign, Ill.: Human
Kinetics, x, 309 p. p.
Rocon, E., J. M. Belda-Lois, A. F. Ruiz, M. Manto, J. C. Moreno and J. L. Pons. 2007.
« Design and Validation of a Rehabilitation Robotic Exoskeleton for Tremor Assessment and Suppression ». Neural Systems and Rehabilitation Engineering, IEEE Transactions on, vol. 15, no 3, p. 367-378.
Rosen, Jacob, Moshe Brand, Moshe B Fuchs and Mircea Arcan. 2001. « A myosignal-based
powered exoskeleton system ». IEEE Trans Systerms, Man, and Cybernetics, vol. 31, no 3, p. 210 - 212.
Sankai, Yoshiyuki. 2006. « Leading Edge of Cybernics: Robot Suit HAL ». In SICE-ICASE,
2006. International Joint Conference. (Bexco, Busan, Korea, 18-21 October 2006), p. P-1-P-2.
Sarakoglou, Ioannis, Sophia Kousidou, Nikolaos G Tsagarakis and Darwin G Caldwell.
2007. « Exoskeleton-based exercisers for the disabilities of the upper arm and hand ». In Rehabilitation Robotics, sous la dir. de Kommu, Sashi S. p. 499-522. I-Tech
132
Education and Publishing. < http://www.intechopen.com/books/rehabilitation_robotics >.
Savitzky, Abraham, and Marcel J. E. Golay. 1964. « Smoothing and Differentiation of Data
by Simplified Least Squares Procedures ». Analytical Chemistry, vol. 36, no 8, p. 1627-1639.
Seamone, W., and G. Schmeisser. 1985. « Early clinical evaluation of a robot arm/worktable
system for spinal-cord-injured persons ». Journal of rehabilitation research and development, vol. 22, no 1, p. 38-57.
Seraji, Homayoun. 1994. « Adaptive admittance control: an approach to explicit force control
in compliant motion ». In 1994 IEEE International Conference on Robotics and Automation. (San Diego, CA., 8-13 May 1994) Vol. 4, p. 2705-2712. IEEE.
Siciliano, Bruno, and Oussama Khatib. 2008. Springer Handbook of Robotics. Berlin,
Heidelberg: Springer Science+Business Media.
Smith, Ryan J., Francesco Tenore, David Huberdeau, Ralph Etienne-Cummings and Nitish
V. Thakor. 2008. « Continuous decoding of finger position from surface EMG signals for the control of powered prostheses ». In 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2008. EMBS 2008. (British Columbia, Canada, 20-24 August 2008), p. 197-200. IEEE.
Song, Zuoshi, Jianqiang Yi, Dongbin Zhao and Xinchun Li. 2005. « A computed torque
controller for uncertain robotic manipulator systems: Fuzzy approach ». Fuzzy Sets and Systems, vol. 154, no 2, p. 208-226.
Sun, F. C., Z. Q. Sun and G. Feng. 1999. « An adaptive fuzzy controller based on sliding
mode for robot manipulators ». Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, vol. 29, no 5, p. 661-667.
Tsagarakis, N., D. G. Caldwell and G. A. Medrano-Cerda. 1999. « A 7 DOF pneumatic
muscle actuator (pMA) powered exoskeleton ». In 8th IEEE International Workshop on Robot and Human Interaction RO-MAN '99. (Pisa, Italy, 27-29 September 1999), p. 327-333. IEEE.
133
Uzmay, Ibrahim, and Recep Burkan. 2002. « Parameter estimation and upper bounding adaptation in adaptive-robust control approaches for trajectory control of robots ». Robotica, vol. 20, no 06, p. 653-660.
Van der Loos, H. Machiel , and David J. Reinkensmeyer. 2008. « Rehabilitation and Health
Care Robotics ». In Springer Handbook of Robotics, sous la dir. de Siciliano, Bruno, and Oussama Khatib. p. 1225-1227. Berlin Heidelberg: Springer. < http://books.google.ca/books?id=Xpgi5gSuBxsC >.
Vitiello, N., T. Lenzi, S. Roccella, S. M. M. De Rossi, E. Cattin, F. Giovacchini, F. Vecchi
and M. C. Carrozza. 2013. « NEUROExos: A Powered Elbow Exoskeleton for Physical Rehabilitation ». Robotics, IEEE Transactions on, vol. 29, no 1, p. 220-235.
Wege, A., K. Kondak and G. Hommel. 2006. « Force Control Strategy for a Hand
Exoskeleton Based on Sliding Mode Position Control ». In Intelligent Robots and Systems, 2006 IEEE/RSJ International Conference on. p. 4615-4620.
Wen-Hua, Chen, D. J. Ballance, P. J. Gawthrop and J. O'Reilly. 2000. « A nonlinear
disturbance observer for robotic manipulators ». Industrial Electronics, IEEE Transactions on, vol. 47, no 4, p. 932-938.
Younggeun, Choi, James Gordon, Kim Duckho and Nicolas Schweighofer. 2009. « An
Adaptive Automated Robotic Task-Practice System for Rehabilitation of Arm Functions After Stroke ». IEEE Transactions on Robotics, vol. 25, no 3, p. 556-568.
Zhang, Bin, Rong Xiong and Jun Wu. 2011. « Kinematics analysis of a novel 7-DOF
humanoid manipulator for table tennis ». In 2011 International Conference on Electronics, Communications and Control (ICECC). (Ningbo, China, 09-11 September 2011), p. 1524-1528. IEEE.
Zhang, Mingming, T Claire Davies and Shane Xie. 2013. « Effectiveness of robot-assisted
therapy on ankle rehabilitation - a systematic review ». Journal of NeuroEngineering and Rehabilitation, vol. 10, p. 30.
Zhijun, Li, S. S. Ge, M. Adams and W. S. Wijesoma. 2008. « Adaptive Robust Output-
Feedback Motion/Force Control of Electrically Driven Nonholonomic Mobile Manipulators ». Control Systems Technology, IEEE Transactions on, vol. 16, no 6, p. 1308-1315.
134
Zhou, Ma, and Pinhas. Ben-Tzvi. 2015. « RML Glove - An Exoskeleton Glove Mechanism With Haptics Feedback ». IEEE/ASME Transactions on Mechatronics, vol. 20, no 2, p. 641-652.
Zhu, Wen-Hong (387-389). 2010. Virtual Decomposition Control: Toward Hyper Degrees of
Freedom Robots. Coll. « Springer Tracts in Advanced Robotics », 60. Berlin Heidelberg: Springer, 448 p.
Zhu, Wen-Hong, and Joris De Schutter. 1999. « Adaptive control of mixed rigid/flexible
joint robot manipulators based on virtual decomposition ». IEEE Transactions on Robotics and Automation, vol. 15, no 2, p. 310-317.
Zhu, Wen-Hong, and Joris De Schutter. 2002. « Experimental verifications of virtual-
decomposition-based motion/force control ». IEEE Transactions on Robotics and Automation, vol. 18, no 3, p. 379-386.
Zhu, Wen-Hong, and Tom Lamarche. 2007. « Modular Robot Manipulators Based on Virtual
Decomposition Control ». In Robotics and Automation, 2007 IEEE International Conference on. (10-14 April 2007), p. 2235-2240.
Zhu, Wen-Hong, Tom Lamarche, Erick Dupuis, David Jameux, Patrick Barnard and Liu
Guangjun. 2013. « Precision Control of Modular Robot Manipulators: The VDC Approach With Embedded FPGA ». IEEE Transactions on Robotics, vol. 29, no 5, p. 1162-1179.
Zhu, Wen-Hong, Jean-Claude Piedboeuf and Yves Gonthier. 2006. « A dynamics
formulation of general constrained robots ». Multibody System Dynamics, vol. 16, no 1, p. 37-54.
Zhu, Wen-Hong, Xi Yu-Geng, Zong-Jun Zhang, Bien Zeungnam and Joris De Schutter.
1997. « Virtual decomposition based control for generalized high dimensional robotic systems with complicated structure ». IEEE Transactions on Robotics and Automation, vol. 13, no 3, p. 411-436.
Zhu, Wen-Hong, Bien Zeungnam and Joris De Schutter. 1998. « Adaptive motion/force
control of multiple manipulators with joint flexibility based on virtual decomposition ». IEEE Transactions on Automatic Control, vol. 43, no 1, p. 46-60.
